Angle Subtended by Chords

Transcript

Angle Subtended by Chords Subtend literally means “opposite to” Thus, Angle subtended by chord is angle made by chord at any point on the circle Here, angle made by chord AB on point P is ∠ APB Now, we have some Theorems related to Angle Subtended by Chord at the center Theorem 2 - Equal chords of a circle subtend equal angles at the centre of the circle In both cases, chords are equal i.e. AB = CD And, angle subtended by them at center is also equal ∠ AOB = ∠ COD Now, we have some Theorems related to Angle Subtended by Chord at the center Theorem 2 - Equal chords of a circle subtend equal angles at the centre of the circle In both cases, chords are equal i.e. AB = CD And, angle subtended by them at center is also equal ∠ AOB = ∠ COD Let’s look at the Proof Proof is here – Theorem 2 of Chapter 5 Class 9 – Ganita Manjari Part 1 Now, let’s look at the next one Theorem 3 - Chords of a circle that subtend equal angles at the centre are equal This is the exact opposite of the previous theorem In both cases, Angle subtended by them at center is equal i.e. ∠ AOB = ∠ COD Thus, chords are equal ∴ AB = CD Let’s look at the Proof Proof is here – Theorem 3 of Chapter 5 Class 9 – Ganita Manjari Part 1