**Q) **In the given figure, ABC is a triangle in which ∠B = 90^{0}, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle.

**Ans: **

By Pythagorus theorem,

AC =

=

=

= 50 cm

**Method 1:**

OP = OQ (radius of a circle)

BP = BQ (tangents from external point)

Since OPBQ is a square, therefore, BP = OQ = r

and BQ = OP = r

Now ∵ BQ = r ∴ AQ = 14 – r

∵ AQ = AR (tangents from external point)

∴ AR = 14 – r …. (i)

Similarly, ∵ BP = r, ∴ CP = 48 – r

∵ CP = CR (tangents from external point)

∴ CR = 48 – r …… (ii)

Since, AC = AR + CR

∴ 50 = (14 – r) + (48 – r)

∴ 50 = 62 – 2 r

∴ 2 r = 12

**∴ r = 6 cm**

**Method 2: **The radius of in-circle of a right angled triangle is given by:

r =

=

=

**= 6 cm**