Question

Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is π/2 and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.

(1) Let a be the area of the triangle ABC. Then the value of (64a)² is _____.

(2) Then the inradius of the triangle ABC is ______.

Answer 1

(1)

Let sides be a – d, a, a + d

A – C = \(\frac \pi 2\)

R = 1

Now

(2)