Theorem 10.9 - Chapter 10 Class 9 Circles (Term 2)
Last updated at Aug. 13, 2018 by Teachoo
Theorems
Theorem 10.1
Theorem 10.2 Important
Theorem 10.3 Important
Theorem 10.4
Theorem 10.5 Deleted for CBSE Board 2022 Exams
Theorem 10.6 Important
Theorem 10.7
Theorem 10.8 Important
Theorem 10.9 You are here
Theorem 10.10 Important
Theorem 10.11
Theorem 10.12 Important
Angle in a semicircle is a right angle Important
Chapter 10 Class 9 Circles (Term 2)
Serial order wise
Transcript
Theorem 10.9 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 10.8: 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.
