Question

The lengths of two tangents drawn from an external point to a circle are _________.

Answer 1

PA and PB are two tangents drawn from P to circle with centre O. OP is the line segment joining the point P and centre of the circle.

In ∆OAP and ∆OBP,

OA = OB (Radius of the circle)

OP = OP (Common)

∠OAP = ∠OBP (Radius is perpendicular to the tangent at the point of contact)

∴ ∆OAP $\cong$ ∆OBP (RHS congruence criterion)

⇒ PA = PB (CPCT)

Hence, the lengths of two tangents drawn from an external point to a circle are equal.


The lengths of two tangents drawn from an external point to a circle are __equal__.