Question

Show that the triangle of maximum area that can be inscribed in a circle is an equilateral triangle.

Answer 1

Let ∆ABC is inscribed in a circle of radius r. A perpendicular E is drawn of AC from the vertex B of triangle which meets AC at D and circle at E.

Let base of triangle AC = 2x

and height of triangle BD = y

So, area of triangle will be maximum

Hence, ∆ABC is an equilateral triangle.