Theorem 9.8 - Chapter 9 Class 9 Circles
Last updated at Feb. 17, 2025 by Teachoo
Last updated at Feb. 17, 2025 by Teachoo
Theorem 9.9 Angles in the same segment of a circle are equal. Given : A circle with center at O. Points P & Q on this circle subtends angles ∠ PAQ and ∠ PBQ at points A and B respectively. To Prove : ∠PAQ = ∠PBQ Proof : Chord PQ subtends ∠ POQ at the center From Theorem 9.8: Angle subtended by an arc at the centre is double the angle subtended by it at any other point on circle ∴ ∠ POQ = 2∠PAQ ∠POQ = 2∠PBQ From (1) and (2) 2∠PBQ = 2∠PAQ ∠ PBQ = ∠PAQ Hence, Proved.
Theorems
Theorem 9.2 Important
Theorem 9.3 Important
Theorem 9.4
Theorem 9.5 Important
Theorem 9.6
Theorem 9.7 Important
Theorem 9.8 You are here
Theorem 9.9 Important
Theorem 9.10
Theorem 9.11 Important
Angle in a semicircle is a right angle Important
Only 1 circle passing through 3 non-collinear points
About the Author
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo