Question

In a right angled triangle ABC, < B= 90°
, AB = 12cm, BC = 16cm. Find the radius of the
circle inscribed in ∆ABC,

Answer 1

Given:

In a right-angled triangle ABC, ∠ B= 90° , AB = 12cm, BC = 16cm

To find:

Find the radius of the  circle inscribed in ∆ABC

Solution:

Here we have given the right-angled triangle, so any of the side this triangle is given by:

By the Pythagoras theorem:

Which stated as sum of the square of the perpendicular and base of the triangle is equal to the square of the hypotenuse of the triangle.

P² + B² = H²

• AB² + BC² = AC²
• 12² + 16² = AC²
• 144 + 256 = AC²
• AC² = 400
• AC = √400
• AC = 20

The circle inscribed in the triangle is called as the incircle fo the triangle

So the inradius of the circle in the right-angled triangle  is given by:

R = (P+B-H)/2

R = (12+16-20)/2

R = 8/2

R = 4

So the inradius of the circle is 4 cm.