# Prove that the largest isosceles triangle that can be drawn in a circle, is an equilateral triangle?

##### 1 Answer

Please see below.

#### Explanation:

Let their be an isosceles triangle ABC inscribed in a circle as shown, in which equal sides

As the area of the triangle portion subtended by an angle

the complete area of triangle ABC is

=

=

=

For maximization we should have

i.e.

or

or

or

or

or

Hence

i.e.

But for a triangle

hence

and hence for maximum area triangle must be equilateral.