Ex 10.2 Q13 Class 10 Math | Ch 10 | Opposite Sides of Quadrilateral Circumscribing Circle Make 180°

In this video, we solve Question 13 (last question) of Exercise 10.2, Chapter 10 – Circles, Class 10 Maths NCERT in a step-by-step and conceptually clear manner in just 3 minutes. 🔹 Question Statement (NCERT): Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. 🔹 Method Used in This Solution: 👉 First, we use the important theorem: “Tangents drawn from an external point are equal in length.” Using this theorem, we form four pairs of triangles around the centre of the circle. 👉 These triangles are proved congruent using the SAS congruence rule, which makes the proof systematic and easy to understand. 👉 Next, we mark the angles at the centre corresponding to these congruent triangles as v, w, x, and y (student-friendly notation). 👉 Since all angles around a point sum to 360°, we get: 2(v+w+x+y)=360° Dividing both sides by 2: v+w+x+y=180° ✔ Hence, we prove that the angles subtended by opposite sides of the quadrilateral at the centre are supplementary. 🎯 Why Watch This Video? ✔ NCERT-based proof explained in simple language ✔ Perfect for Class 10 board exam preparation ✔ Helps students understand circle theorems clearly ✔ Very useful for geometry proofs & concept clarity 👨‍🎓 This Video Is Useful For: • Class 10 Maths students (CBSE / State Boards) • Students struggling with geometry proofs • Learners preparing for board exams • Anyone who wants to understand circles chapter deeply • For SSC, BANK PO, RAILWAY and other Government JOBS exams 📌 Tip: Watch till the end to understand how angle sum concept + congruent triangles work together in circle proofs. #lastquestionexercise10_2 #exercise10_2question13 #supplementaryangles #ncertsolutions #class10maths