JEE Main Maths: Triangles / Circles (Geometry) questions with solutions

Q1. PQR is a right-angled triangle (right angle at Q) with PQ = 12 cm and QR = 5 cm. A circle of radius x is inscribed in the triangle. Find x.

1. 2 cm
2. 1 cm
3. 3 cm
4. 4 cm

Answer: 2 cm

The hypotenuse PR = sqrt(12² + 5²) = 13 cm. For a right triangle, the inradius equals (leg1 + leg2 - hypotenuse)/2 = (12 + 5 - 13)/2 = 4/2 = 2 cm.