Question

prove that the tangents which are drawn from an external point to the circle are equal​

Answer 1

To proof :

Tangents drawn from an external point to a circle are equal.

Given:

In a circle AP and PB are two tangednts from external point P.

To prove :

AP = AN

Construction :

Join PO, OB, OA

Now

as we know that tangents at any point of a circle is perpendicular to the radius through the point of contact.

OA ⊥ AP and OB ⊥ BP

so,

∠PAO = ∠PBO = 90°

now

OA = OB (radii of circle)

OP = OP (common side)

So

by RHS congruence rule.

ΔAPO ≅ ΔBPO

hence

by CPCT AP = BP

Hence Proved