Question

29. Prove that the tangents drawn to a circle from an external point are equal.​

Answer 1

Answer:

Theorem

The length of the tangents drawn from an external point to a circle are equal.

Proof

Given a circle with a centre O, P is a point lying outside the circle. PQ & PR are two tangents from the point P.

To prove that : PQ = PR

We want to join centre O to the points Q & P

OR join OQ, OR

Also want to join point P and centre O .i. e., join OP.

Then consider POQ &POR

Angle PQO = Angle PRO [90° because tangents are perpendicular to the radius]

OQ = OR [Radii]

OP = OP [common]

By RHS Congruence rule

POQ congruent to the POR

PQ = PR (CPCT)

Therefore lengths of tangents drawn from an external points to a circle are equal.

I hope this will help u. Please mark me as a brainliest.

Answer 2

STATEMENT: The tangents drawn from an external point are equal....

GIVEN: In a circle,

O is the centre of the circle

P is a point away from the circle

PQ and PR are the tangents

TO PROVE: PQ=PR

CONSTRUCTION: Join OQ and OR and also PO

PROOF:

QOP= POR

OP=OP

OR=OQ