Question

Prove that the tangents drawn at the ends of a chord of circle make equal angles with the chord.

Answer 1

Given:- A circle with center O, PA and PB are tangents drawn at ends A and B on chord AB.

To prove:- ∠PAB = ∠PBA

Construction:- Join OA and OB

Proof:- In △AOB

OA = OB (Radii of the same circle)

∠OAB = ∠OBA  .....(i) (Angles opposite to equal sides)

∠OAP = ∠OBP = 90 (∵ Radius ⊥ Tangent)

⇒ ∠OAB + ∠PAB = ∠OBA + ∠PBA

⇒ ∠OAB + ∠PAB = ∠OAB + ∠PBA (From eq (i))

⇒ ∠PAB = ∠PBA

Hence proved.

Answer 2

Answer is........