Circle Class 10 | Inscribed Angle Theorem + Corollaries 🔥 | Important Proofs & Sums | Lecture 7

🔥 *MASTER THE INSCRIBED ANGLE THEOREM! | CLASS 10 CIRCLE* In this lecture, we continue the *Circle chapter* and build on the *Inscribed Angle Theorem* to solve important exam-oriented problems. You’ll learn how to identify and apply **Central Angles, Inscribed Angles, Corollaries, Semicircle → 90°**, and use these concepts in challenging proof-based questions. We also solve important problems involving **tangents, diameters, perpendiculars, chords and similar triangles**—exactly the kind of concepts that can make Circle questions much easier in exams. 💡 *Key concepts covered:* ✅ Central Angle & Minor Arc ✅ Inscribed Angle Theorem ✅ Angles Inscribed in the Same Arc ✅ Angle Inscribed in a Semicircle = 90° ✅ Corollaries of the Inscribed Angle Theorem ✅ Tangent & Radius Relationship ✅ Chord and Diameter Concepts ✅ Similarity of Triangles ✅ Important Circle Proofs ✅ Exam-oriented Problem Solving 🎯 *Best for:* Class 10 Mathematics | CBSE | ICSE | SSC | Maharashtra Board ⏱️ *TIMESTAMPS* 00:00 – Introduction to the Circle Lecture 00:30 – Revision of Inscribed Angle Theorem 01:03 – Central Angle & Minor Arc 02:08 – What is an Inscribed Angle? 02:49 – Inscribed Angle Theorem 03:24 – Important Circle Problem Begins 03:55 – Using Radius & Chord Concepts 04:36 – Proving the Triangle is Equilateral 05:04 – Finding the Central Angle 06:34 – Applying the Inscribed Angle Theorem 07:19 – Finding the Inscribed Angle 07:26 – Finding the Major Arc 08:07 – Final Solution & Key Takeaways 08:49 – Introduction to Corollary 09:01 – What is a Corollary? 09:35 – Angles Inscribed in the Same Arc 10:20 – Understanding the Same Arc Concept 11:30 – Proving Angles are Congruent 13:04 – Why All Angles in the Same Arc are Equal 14:18 – Second Important Corollary 14:25 – Angle Inscribed in a Semicircle 14:43 – What is a Diameter? 15:15 – Semicircle Angle = 90° 16:20 – Proof of the Semicircle Corollary 18:20 – Proving 90° Using the Inscribed Angle Theorem 19:10 – Important Circle Proof Question 19:21 – Two Internally Touching Circles 20:03 – Proving EA = AB 20:28 – Theorem of Touching Circles 21:05 – Identifying the Semicircle 21:36 – Getting the 90° Angle 22:14 – Perpendicular to the Chord 23:12 – Applying the Chord Bisector Theorem 25:21 – Complete Proof Strategy 25:58 – ⭐ IMPORTANT EXAM QUESTION 26:07 – Diameter & Exterior Point Problem 26:36 – Proving an Acute Angle 27:18 – Semicircle → 90° Trick 28:06 – Construction for the Proof 29:05 – Applying the Semicircle Theorem 30:05 – Exterior Angle Theorem 31:21 – Proving the Angle is Less Than 90° 32:13 – Final Result: Acute Angle 33:57 – ⭐ Another Important Circle Problem 34:10 – Diameter + Tangent Problem 34:56 – Proving DE × GE = 4R² 35:20 – The Key Algebraic Transformation 35:38 – Using the Diameter 36:05 – Creating the Required Ratio 36:42 – Connecting the Problem to Similarity 37:24 – ⭐ Similarity Trick 37:49 – Construction: Joining GF 39:17 – Finding the Common Angle 39:32 – Getting the Second 90° Angle 40:14 – Starting the Formal Proof 41:05 – Tangent Theorem Application 41:27 – Proving the Triangles Similar 42:27 – Corresponding Sides & Ratios 43:03 – Cross Multiplication 43:22 – Final Result: DE × GE = 4R² 44:04 – Exam Strategy & Key Takeaways 44:44 – Next Lecture Preview 45:00 – Like, Share & Subscribe 🔥 *If you found this lecture useful, LIKE the video, SUBSCRIBE to Raakesh Sangha Maths Simplified, and SHARE it with your classmates!* #Class10Maths #Circle #InscribedAngleTheorem #CircleTheorem #Maths #ICSE #CBSE #MaharashtraBoard #SSC #Geometry