Question

there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.



OR

Prove that the tangents drawn at the end-points of a chord of a circle make equal angles with the chord.

there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS.



OR

Prove that the tangents drawn at the end-points of a chord of a circle make equal angles with the chord.

​

Answer 1

Question;

Prove that the tangents drawn at the end-points of a chord of a circle make equal angles with the chord.

ANSWER;

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, we have

OA=OB(Radii of the same circle)

∠OAB=∠OBA.....(1)(Angles opposite to equal sides)

∠OAP=∠OBP=90(∵Radius⊥Tangent)

⇒∠OAB+∠PAB=∠OBA+∠PBA

⇒∠OAB+∠PAB=∠OAB+∠PBA(From (1))

⇒∠PAB=∠PBA

Hence proved.