Question

proove that length of tangents drawn from an external point to a circle are equal​

Answer 1

Answer:

Given: PQ and PR are tangents from an external point P to the circle with centre O.

To prove: PQ = PR

Construction: Join O to P, Q, and R

Proof: In ΔOPQ and ΔOPR,

⇒ OQ = OR [radii of same circle]

⇒ OP = OP [Common]

∴ ΔOPQ ≅ ΔOPR [R.H.S.]

This gives, PQ = PR [By CPCT]

Ans. Hence, the length of the tangents drawn from an external point to a circle is equal.