Theorems

Theorem 9.1

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 Deleted for CBSE Board 2024 Exams

Last updated at April 16, 2024 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.