Question

∆LMN is a right angled triangle with ∠L = 90°. A circle is inscribed in it. The lengths of the sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle.

Answer 1

LN = 6; ML = 8.

In the right ∆LMN,

MN² = LN² + LM²

= 6² + 8² = 36 + 64 = 100

MN = `sqrt(100)` = 10

OA = OB = OC = r

AN = CN  ...(Tangent of the circle)

LN – AL = CN

LN – r = CN

8 – r = CN   ...(1)

MC = MB  ...(Tangent of the circle)

MC = ML – LB

MC = 6 – r  ...(2)

Add (1) and (2)

MC + CN = (6 – r) + (8 – r)

MN = 14 – 2r

10 = 14 – 2r

2r = 14 – 10 = 4

r = `4/2` = 2 cm

radius of the circle = 2 cm