The lengths of tangents of drawn from an external point to a circle are equal.Proof: we are given a circle with centre $O$ , a point $P$ lying outside the circle and two tangents $P Q, P R$ on te circle from $P$ . We are required to prove that $P = P R$ For this, we join $O P, O Q$ and $O R$ . Then $∠ O Q R$ and $∠ O R P$ are right angles, because these are angles between the radii and tangents, and according to Theorem $10.1$ they are right angles. Now in right triangles $O Q P$ and $O R P$

Question

The lengths of tangents of drawn from an external point to a circle are equal.Proof: we are given a circle with centre

O

, a point

P

lying outside the circle and two tangents

P Q, P R

on te circle from

P

. We are required to prove that

P = P R

For this, we join

O P, O Q

and

O R

. Then

∠ O Q R

and

∠ O R P

are right angles, because these are angles between the radii and tangents, and according to Theorem

10.1

they are right angles. Now in right triangles

O Q P

and

O R P

Toppr Admin · Accepted Answer

The correct options are A OQ-OR B OP-OP C -x25B3-OQP-x2245-x25B3-ORP D PQ-PR