# In triangle ABC, AB=AC.The circle through B touches the side AC at the mid-point D of AC, passes through a point P on AB. Prove that 4 ×AP = AB ?

##### 1 Answer

Apr 19, 2017

see explanation.

#### Explanation:

According to tangent-secant theorem:

"When a tangent and a secant are drawn from one single external point to a circle, square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment."

Given

Hence