Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is \(\frac{\pi}{2}\) and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1. Then the inradius of the triangle ABC is

Properties of Triangle — JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 Question with Solution

\frac{π}{2}

QR = 1

∠ P QR = ∠ QR S = 7 0^{\circ}

∠ P QS = 1 5^{\circ}

∠ P R S = 4 0^{\circ}

∠ R P S = θ^{\circ}

P Q = α

P S = β

A B = 23, B C = 3

C A = 4

\frac{c o t A + c o t C}{c o t B}

tan \frac{X}{2} + tan \frac{Z}{2} = \frac{2 y}{x + y + z},

Δ PQR