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video, \"Pratik Bilgiler\" serisinin bir bölümü olup, bir eğitmen tarafından sunulan teknik bir eğitim içeriğidir.","Video, şekil değiştirmeye göre değerlendirme yaklaşımında kiriş kesitinin nasıl modelleneceğini göstermektedir. Eğitmen, 60x80 inç boyutlarındaki dikdörtgensel bir kiriş kesitinin SAP2000 programında nasıl tanımlanacağını adım adım anlatmaktadır. Önce kesit özellikleri (donatılar, mesnet bölgesi, gövde donatıları) tanımlanmakta, ardından Section Designer kullanılarak kesit modeli oluşturulmaktadır. Video, kesit modelinin oluşturulmasıyla sona ererken, bir sonraki derste kesit özellikleri inceleneceği belirtilmektedir."]},"endTime":476,"title":"Kiriş Kesiti Modelleme Eğitimi","beginTime":0}],"fullResult":[{"index":0,"title":"Kiriş Kesiti Tanıtımı","list":{"type":"unordered","items":["Video serisinin yeni bölümünde şekil değiştirmeye göre değerlendirme yaklaşımında malzeme tanımı ve beklenen dayanımların nasıl dikkate alınacağı gösterilecektir.","Bu bölümde kiriş kesiti nasıl modelleneceği ve sargı donatısı nasıl tarif edileceği gösterilecektir.","Kiriş kesiti 60 mm genişliğinde, 80 mm yüksekliğinde olup, dört kol ve iki etriye sahiptir."]},"beginTime":11,"endTime":75,"href":"/video/preview/13164019685289537937?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=11&ask_summarization=1"},{"index":1,"title":"Kesit Tanımlama","list":{"type":"unordered","items":["SAP2000 açılırken Section Properties menüsünden Frame Section 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Kiriş örneği üzerinden kavramlar somutlaştırılmakta ve \"sabit mesnetler iki reaksiyon kuvveti\" gibi hatırlatıcı ifadeler sunulmaktadır."]},"endTime":1576,"title":"İnşaat Mühendisliğinde Mesnet ve Kiriş Kavramları","beginTime":0}],"fullResult":[{"index":0,"title":"Kirişler ve Özellikleri","list":{"type":"unordered","items":["Kiriş, boyuna göre eksenetik kuvvetin etkisi altında bulunan yatay beton çubuklardır ve kolonları yatayda birbirine bağlarlar.","Kirişler eğilmeye ve bükülmeye dayanıklı olmalı ve taşıdıkları yükü düşey taşıyıcılara dengeli bir şekilde aktarmalıdır.","Kirişler geometrisine, denge durumuna, insaat yöntemine, destek koşullarına, yapı malzemelerine ve kesit şekillerine göre sınıflandırılabilirler."]},"beginTime":41,"endTime":116,"href":"/video/preview/7983864011335011709?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=41&ask_summarization=1"},{"index":1,"title":"Kirişlerin Önemi ve Hasarları","list":{"type":"unordered","items":["Depremlerden ve diğer afetlerden en çok etkilenen yapı elemanları kirişlerdir.","Deprem durumunda kiriş kesitlerinde farklı gerilme olayları meydana gelir ve donatının birleşim yerlerinden çekilmesine yol açabilir.","Kirişler yapıların en önemli yapı organlarından biridir ve bir binanın ayakta kalmasını sağlayan yegane unsurdur."]},"beginTime":116,"endTime":350,"href":"/video/preview/7983864011335011709?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=116&ask_summarization=1"},{"index":2,"title":"Denge Denklemleri","list":{"type":"unordered","items":["İki boyutlu bir yapının herhangi bir yönde hareket etmemesi için birbirine dik herhangi iki yönde hareket etmemesi gerekir.","Yatay ve dikey yönde hareket olmaması için o yönlerde etki eden kuvvetlerin toplamı sıfır olmalıdır.","Düzlemde dönme olmaması için herhangi bir noktada momentlerin toplamı sıfıra eşit olmalıdır."]},"beginTime":350,"endTime":555,"href":"/video/preview/7983864011335011709?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=350&ask_summarization=1"},{"index":3,"title":"Mesnet Nedir?","list":{"type":"unordered","items":["Mesnet, anlaması güç olmasa da dayanak ve destek anlamına gelir.","Mesnetler, bir elemanın düşey ve yatay doğrultuda hareket etmesini ve dönmesini engelleyen sistemlerdir.","Mesnetler yapıya destek olur ve üzerine gelen yükleri taşıyabilmesini sağlar."]},"beginTime":555,"endTime":645,"href":"/video/preview/7983864011335011709?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=555&ask_summarization=1"},{"index":4,"title":"Mesnet Çeşitleri","list":{"type":"unordered","items":["İnşaatlarda farklı noktalarda dayanak için çeşitli mesnet çeşitleri kullanılır.","En yaygın mesnet çeşitleri ankastre mesnet, sabit mesnet, hareketli mesnet, pandül ve elastik ankastre mesnet olarak sıralanabilir."]},"beginTime":645,"endTime":675,"href":"/video/preview/7983864011335011709?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=645&ask_summarization=1"},{"index":5,"title":"Mesnetlerin Türleri ve Önemi","list":{"type":"unordered","items":["Mesnetler, inşaatlarda dayanak amaçlı veya dekoratif olarak kullanılan farklı boyutlarda ve şekillerde değişik tiplerden oluşmaktadır.","Pandül mesnet, pandül ayak ve elastik ankastre mesnet gibi çeşitler vardır; 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anlatılmaktadır. Eğitmen önce kapalı ve açık yöntemler arasındaki farkları açıklamakta, ardından kiriş metodunun matematiksel temelini, algoritmasını ve uygulamasını grafiklerle destekleyerek göstermektedir.","Video, kiriş metodunun adım adım uygulanması, yakınsama ve ıraksama durumları, hata analizi gibi konuları içermektedir. Ayrıca, düşen cismin ağırlığını bulma problemi üzerinden pratik bir örnek çözümü sunulmakta ve öğrencilere MatLab veya Excel programında bu problemi çözerek virgülden sonra dört basamak hassasiyette sonuç bulmaları için ödev verilmektedir."]},"endTime":3583,"title":"Kiriş Yöntemi ile Sayısal Kök Bulma Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Sayısal Kök Bulma Teknikleri","list":{"type":"unordered","items":["Cebirsel denklemlerin köklerini bulmak için sayısal kök bulma teknikleri kullanılır.","Sayısal kök bulma teknikleri ikiye ayrılır: kapalı yöntemler ve açık yöntemler."]},"beginTime":1,"endTime":27,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=1&ask_summarization=1"},{"index":1,"title":"Kapalı ve Açık Yöntemlerin Farkları","list":{"type":"unordered","items":["Kapalı yöntemlerde kök iki değer arasında kıskaca alınır ve bu aralıkta kök tahmin edilir.","Kapalı yöntemlerde kökün sıkıştığı aralık (delta aralığı) işlem sonunda daraltılır ve gerçek köke sayısal olarak yaklaşılmaya çalışılır.","Açık yöntemlerde ise kökler bir değer üzerinden iterasyonlarla (aynı işlemler tekrarlanarak) bulunur ve tahmini başlangıç değeri her adımda aynı işlemlere sokulur."]},"beginTime":27,"endTime":165,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=27&ask_summarization=1"},{"index":2,"title":"Sayısal Yöntemlerin Özellikleri","list":{"type":"unordered","items":["Her iki yöntemde de köke sayısal olarak yakınsama gerçekleşir, ancak mantıkları birbirinden farklıdır.","Kapalı yöntemlerde kıskaca alınan bölge iyice daraltılırken, açık yöntemlerde belli bir tahmini değerden başlanarak iterasyonlar yapılır.","İki bölme tekniği, fonksiyonun işaret değişimine bakarak kökü bulan bir kapalı yöntemdir."]},"beginTime":165,"endTime":281,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=165&ask_summarization=1"},{"index":3,"title":"Sayısal Yöntemlerin Uygulanması","list":{"type":"unordered","items":["Sayısal yöntemlerde en iyi metot diye bir şey yoktur, her problem için uygun metot seçilmelidir.","Ders kapsamında verilen sorular belirli tekniklerle çözülecek, ancak gerçek hayatta problem analiz edilerek uygun sayısal yaklaşım seçilmelidir.","Öğrencilerden verilen yöntemleri uygulamaları ve belirli hata hassasiyetine ulaşmaları beklenir."]},"beginTime":281,"endTime":394,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=281&ask_summarization=1"},{"index":4,"title":"Kiriş Yöntemi (Regula Falsi)","list":{"type":"unordered","items":["Kiriş yöntemi, kapalı yöntemlerden biridir ve kökün yerini doğru tahmin etmek için fonksiyondaki işaret değişimine bakar.","Kökün yerini tahmin etmek için fonksiyonun değerinin negatif ve pozitif olduğu iki y(x) değeri tespit edilir.","Kiriş yönteminde, iki noktadan geçen bir doğru çizilir ve bu doğrunun x eksenini kestiği nokta yaklaşık sayısal kök olarak kabul edilir."]},"beginTime":394,"endTime":638,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=394&ask_summarization=1"},{"index":5,"title":"Kiriş Yönteminde İterasyon","list":{"type":"unordered","items":["Kiriş yönteminde, yeni kök tahmini için önceki tahminlerden biri ile fonksiyonu aynı işaretli yapan değer yeni alt nokta olarak alınır.","Her adımda fonksiyonun hangi değeriyle (üst ile mi alt değeri ile mi) aynı işaretli yaptığı kontrol edilir.","Bu yöntemle kök tahmini sürekli olarak daraltılan aralıkta bulunur ve köke yakınsama gerçekleşir."]},"beginTime":638,"endTime":982,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=638&ask_summarization=1"},{"index":6,"title":"Kiriş Metodu ve Tanjant Hesaplaması","list":{"type":"unordered","items":["İki üçgen üzerinden tanjant alfa hesaplaması yapılıyor: büyük üçgende tanjant alfa = fx üst / (x - xr), küçük üçgende tanjant alfa = fx alt / (xr - x alt).","İki denklem eşitlenerek xr değeri bulunuyor: xr = x - (fx alt * (x alt - x)) / (fx üst - fx alt).","Kiriş metodu ile kök bulma işlemi, fonksiyonu ters işaretli yapan x3 ve xa değerlerini belirleyip, denklem yıldızından xr hesaplayarak tekrarlanır."]},"beginTime":999,"endTime":1522,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=999&ask_summarization=1"},{"index":7,"title":"Kiriş Metodu Algoritması","list":{"type":"unordered","items":["Kiriş metodunun algoritması: 1) Fonksiyonu ters işaretli yapan x3 ve xa belirle, 2) Denklem yıldızdan xr hesapla, 3) Hesaplanan xr değerini fonksiyonu xa veya x3 ile aynı işaretli yapan değerle yer değiştir.","Hata analizi için iki kontrol algoritması kullanılır: 1) Hata toleransı altına düşerse işlem sonlandırılır, 2) Maksimum döngü sayısı atlanırsa işlem sonlandırılır.","İyi bir tahmini başlangıç şartıyla en fazla 10-15 döngüde hata kriteri sağlanır, 50 adımda da sağlanmazsa işlem sonlandırılır."]},"beginTime":1522,"endTime":2013,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=1522&ask_summarization=1"},{"index":8,"title":"Kiriş Metodu Örneği","list":{"type":"unordered","items":["Hava sürtünmesine maruz serbest düşen bir cismin hızı formülü: v = √(g*m/c) * tanh(√(g/c)*t).","Verilen değerler: c = 0,25, t = 4 saniye, v = 36 m/s, g = 9,81 m/s² kullanılarak m kütlesi bulunacak.","Denklem standart formda gösterilerek fm = √(39,24m) * tanh(√(2,45m) * 4) - 36 şeklinde yazılır ve fm fonksiyonunun kökü aranır."]},"beginTime":2013,"endTime":2293,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=2013&ask_summarization=1"},{"index":9,"title":"Kiriş Yöntemi ve Kök Bulma","list":{"type":"unordered","items":["Fonksiyonun işaret değişimi önemlidir; kökten önce negatif, kökten sonra pozitif değerler bulunur.","Kiriş (yer değiştirme) metoduyla denklemi çözerken, f(x) fonksiyonunu ters işaretli yapan x alt ve x üst değerleri belirlenmelidir.","m alt=50 ve m üst=200 değerleri seçildiğinde, f(50)=-4,5794 ve f(200)=0,863 değerleri elde edildi, bu da f(50)×f(200)\u003c0 olduğundan kökün bu aralıkta olduğunu gösterir."]},"beginTime":2300,"endTime":2483,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=2300&ask_summarization=1"},{"index":10,"title":"Kiriş Yönteminin Uygulanması","list":{"type":"unordered","items":["Kiriş metodunun formülü m cinsinden modifiye edilerek kullanılacak ve virgülden sonra dört basamak hassasiyette işlem yapılacaktır.","İlk döngüde m_re=176,2773 kg değeri hesaplandı ve f(m_re)=0,5662 pozitif olduğundan, m_re yeni m_üst değeri olarak atandı.","İkinci döngüde m_re=162,3828 kg değeri bulundu ve f(m_re)=0,3576 pozitif olduğundan, bu değer yeni m_üst değeri olarak atandı."]},"beginTime":2483,"endTime":3072,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=2483&ask_summarization=1"},{"index":11,"title":"Yakınsama Süreci","list":{"type":"unordered","items":["Üçüncü döngüde m_re=154,2445 kg değeri bulundu ve f(m_re)=0,2194 pozitif olduğundan, bu değer yeni m_üst değeri olarak atandı.","Dördüncü döngü sonunda m_re=149,4777 kg değeri bulundu.","Yakınsama çok yavaş gerçekleşiyor çünkü aralık geniş tutulmuş ve kiriş metodu ilkel bir metottur."]},"beginTime":3072,"endTime":3333,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=3072&ask_summarization=1"},{"index":12,"title":"Fiziksel Altyapı ve Tahmin Değerleri","list":{"type":"unordered","items":["Mühendisler için sayısal yöntemler dersindeki soruların büyük çoğunluğu fiziksel altyapıya sahiptir.","Fiziksel altyapı bilgisi sayesinde çözümün nerede olacağı tahmin edilebilir.","Düşen cismin ağırlığını tahmin etmek için fiziksel altyapı bilgisine dayanmak avantaj sağlar."]},"beginTime":3337,"endTime":3435,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=3337&ask_summarization=1"},{"index":13,"title":"Kiriş Yöntemi Sonuçları","list":{"type":"unordered","items":["Düşen cismin ağırlığının 50 ile 200 kilogram arasında olduğu tahmin edilerek başlanmıştır.","İlk kiriş yöntemi döngüsünde 176,27 ve 73 değerleri bulunmuştur.","Üç adımda 142,73 ve 76 değerlerine yakınsama sağlanmıştır."]},"beginTime":3435,"endTime":3486,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=3435&ask_summarization=1"},{"index":14,"title":"Hassasiyet ve İşlemler","list":{"type":"unordered","items":["Soruda virgülden sonra dört basamak hassasiyette çözümler istenmemiştir.","İşlemlerde virgülden sonra dört basamak alınması ve dört iterasyon sonucu bulunması istenmiştir.","Virgülden sonra dört basamak hassasiyette çözüm istenirse, en az beş veya altı basamak çalışıp sonucu dört basamağa yuvarlamak tavsiye edilir."]},"beginTime":3486,"endTime":3547,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=3486&ask_summarization=1"},{"index":15,"title":"Ödev","list":{"type":"unordered","items":["Öğrencilerden bir bilgisayar programı yazılması istenmiştir.","Matlap veya Excel kullanılarak virgülden sonra dört basamak hassasiyette sonuç bulunması gerekmektedir.","Bulunan sonuçlar sistemine yüklenebilir."]},"beginTime":3547,"endTime":3578,"href":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=3547&ask_summarization=1"}],"linkTemplate":"/video/preview/8270718916860986116?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Kiriş veya yer değiştirme (regula falsi ) yöntemi ile cebirsel denklemin sayısal çözümü","related_orig_text":"Cuneyit Kiris","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Cuneyit 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bir kirişin kuvvet ve moment diyagramının elde edilmesi...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3046380/4f75cedfef10f547abe4a5d8aa59c64f/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/IoOcJAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"16","reqid":"1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=videoid:2221397239232413051","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitim içeriği olup, bir eğitmen tarafından kiriş probleminin çözümü adım adım anlatılmaktadır.","Video, bir kiriş probleminin kesit tesirlerini (kesme kuvveti ve moment) elde etme sürecini kapsamaktadır. Önce mesnet reaksiyon kuvvetlerinin belirlenmesi, ardından kesme yöntemi kullanılarak kirişin iki kesite bölünmesi ve her kesit için kuvvet ve moment ifadelerinin elde edilmesi gösterilmektedir. Son olarak, elde edilen kesme kuvveti ve moment değerlerinin çizilerek kesme diyagramı oluşturulmaktadır."]},"endTime":621,"title":"Kiriş Problemi Çözümü: Kesit Tesirleri ve Kesme Diyagramı","beginTime":0}],"fullResult":[{"index":0,"title":"Mesnet Reaksiyon Kuvvetlerinin Belirlenmesi","list":{"type":"unordered","items":["Kesit tesirlerini (kuvvet ve moment) elde etmek için öncelikle mesnet reaksiyon kuvvetlerini belirlemek gerekir.","A mesneti sabit mesnet olduğu için Fy düşey ve Fx yatay reaksiyon kuvvetleri olacaktır.","C mesneti hareketli mesnet olduğu için sadece düşey kuvvete maruz kalacaktır."]},"beginTime":5,"endTime":39,"href":"/video/preview/2221397239232413051?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=5&ask_summarization=1"},{"index":1,"title":"Denge Denklemlerinin Yazılması","list":{"type":"unordered","items":["Toplam Fy + Fc = P denklemi elde edilir, burada iki bilinmeyen vardır: Fy ve Fc.","İkinci denge denklemi moment ifadesinden elde edilir ve Fc'ler sadeleşerek Fy = P/2 olarak bulunur.","Kuvvetin tam orta noktasından etki ettiği için kuvvetin yarısı A mesnetine, diğer yarısı C mesnetine taşınır."]},"beginTime":39,"endTime":124,"href":"/video/preview/2221397239232413051?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=39&ask_summarization=1"},{"index":2,"title":"Kesme Yöntemi ve Kesit Analizi","list":{"type":"unordered","items":["Kesme yöntemi kullanarak kuvvetin farklılaştığı bölgelerden kesit alınır ve problem iki kesite bölünür.","Birinci kesit için Fy = V1 denklemi elde edilir ve V1 = P/2 olarak bulunur.","Birinci kesit bölgesindeki moment ifadesi M1 = (P/2) × x olup, geçerli aralığı 0 ≤ x ≤ 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Eğitmen, çemberde kiriş konusunu ve ilgili problemleri anlatmaktadır.","Videoda çemberde kiriş kavramı tanımlanarak başlanmakta ve merkezden kirişe indirilen dikmenin kirişi ve yayı iki eşit parçaya böldüğü açıklanmaktadır. Eğitmen, çemberin yarıçapını bulma, kiriş uzunlukları ve çevre açıları gibi konuları çeşitli örnek sorular üzerinden pekiştirmektedir.","Çözümlerde özel üçgenler (6-8-10, 3-4-5, 8-15-17, 30-60-90, 5-12-13) ve Pisagor teoremi kullanılarak adım adım çözüm adımları gösterilmektedir. Dik üçgenlerde 90'ın karşısındaki kenarın karesi, dik kenarlardan birinin karesi ve diğerinin karesi eşit olduğu kuralı da açıklanmaktadır."]},"endTime":1445,"title":"Çemberde Kiriş Konusu ve Problemleri Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Kiriş Kavramı ve Özellikleri","list":{"type":"unordered","items":["Kiriş, çemberin merkezinden indirilen dikme kirişi ve yayı ortalar.","Merkezden kirişe indirilen dikme kirişi iki eşit parçaya böler.","Çemberde çapı gören çevre açı her zaman 90 derecedir."]},"beginTime":0,"endTime":36,"href":"/video/preview/2825182185340007841?parent-reqid=1769482417828274-10619167461291157062-balancer-l7leveler-kubr-yp-klg-73-BAL&text=Cuneyit+Kiris&t=0&ask_summarization=1"},{"index":1,"title":"Çemberde Kiriş Problemleri","list":{"type":"unordered","items":["İlk soruda, merkezden kirişe indirilen dikme kirişi iki eşit parçaya böler ve özel üçgenler kullanılarak çemberin yarıçapı 10 santimetre olarak bulunur.","İkinci soruda, merkezden 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