Tangets from external point to the circle are equal

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

Answer:

Given :

Let AP and BP be the two tangents drawn from external point P to the circle with centre O.

To Prove : AP = BP

Proof :

In $\Delta$ AOP and $\Delta$BOP

OA = OB (radii) 

$\angle OAP=\angle OBP={90}^{\circ }$ 

(Line drawn from from center to the tangent through the point of contact is perpendicular) 

OP = OP (common)

$\therefore \Delta AOP\cong \Delta BOP$ (R.H.S.) 

$\therefore$ AP = BP ( C P C T ) 

Therefore the length of the

 tangents drawn from an

 external point to a circle are

 equal.