ABC is a right angled triangle right angled at B. A circle with centre O inscribed in the triangle. AB=6CM BC=8CM. Find the radius r of the circle

Radius = 2 cm.

Step by step explanation:

By the Pythagoras theorem the third side of the triangle

= sqrt (6^2 + 8^2) cm = sqrt100 = 10cm.

The formula for the radius of the circle is

r = sqrt [ (s - a) (s-b) (s-c) / s ] where a, b, c are side lengths and s = the semi perimeter.

Here s = (6+8+10) / 2 = 12

So the radius r

= sqrt [ (12-6) (12-8) (12-10) / 12 ]

= sqrt 4

= 2 (answer).