Geometry (C10)

In Figure, ABC is a triangle in which ∠B = 90º, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle.

Answer

AC = √(AB2 + BC2)

=√(142 + 482)

= 50 cm

∠OQB = 90°

⇒ OPBQ is a square

⇒ BQ = r, QA = 14 – r = AR

Again PB = r,

PC = 48 – r

⇒ RC = 48 – r

AR + RC = AC

⇒ 14 – r + 48 – r = 50

⇒ r = 6 cm