ABC is a right angled triangle, right angled at B with AB = 3 cm and BC = 4 cm. A circle which touches all the sides of the triangle is inscribed in the triangle. Calculate the radius of the circle.
Given that AB = 3 cm, BC = 4 cm
Applying Pythagoras theorem to △ABC we get
AC2 = AB2 + BC2
AC2 = 32 + 42
AC2 = 25
AC = 5 cm
Let AQ = AP = l, BQ = BR = n, CR = CP = m
l+n=3 ……(i)
n+m=4 ⇒ n=4-m
Substituting in (i)
l+4-m=3
l-m=-1 …..(ii)
l+m=5 ….(iii)
Adding (ii) and (iii)
2l=4
l=2
n=1
But n=x i.e. the radius of the circle
Therefore the radius of the circle is 1 cm.