Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

Suppose,

   

and circle with

   

as diameter is drawn which intersects the side

   

And, join

   

Proof:

It’s seen that,

   

 [Angle in a semi-circle]

And,

   

[Linear pair]

Thus,

   

Now, in right

   

   

[Given]

   

[Common]

   

Hence, by R.H.S criterion of congruence.

   

Now, by CPCT

   

Therefore,

   

is the mid-point of