Question

An isosceles triangle of vertical angle 2θ is inscribed in a circle of radius a. Show that the area of triangle is maximum when θ = π/6.

Answer 1

Let ABC be an isosceles triangle inscribed in the circle with radius a such that AB = AC. AD = AO + OD = a + a cos2θ and BC = 2BD = 2a sin2θ (see fig. 16.4)