△ABC is a right- angled triangle with AB = 12 cm and AC = 13 cm. A circle with center O has been inscribed inside the triangle. Calculate the radius of the inscribed circle.
Given that AB = 12 cm, AC = 13 cm
Applying Pythagoras theorem to △ABC
BC2 = AC2 – AB2
BC2 = 132 - 122
BC = 5 cm
Let AQ = AP = l, BQ = BR = n, CR = CP = m
l+n=12 …..(i)
n+m=5⇒ n=5-m
Equation (i) becomes l+5-m=12
l-m=7 …..(ii)
l+m=13 …..(iii)
Adding (ii) and (iii)
2l=20
l=10
n=2
But n= radius of the circle
Therefore the radius of the circle is 2 cm.