Question

ABC is a right angled triangle with BC = 6cm and AB = 8cm . A circle with centre O and radius r cm has been inscribed in triangle ABC. find the value of r.

Answer 1

In right triangle BAC
BC2 = AB2 + AC2 [By Pythagoras theorem]
= 62 + 82
= 36 + 64
= 100
Hence BC = 10 cm
Semi-perimeter, s = (a + b + c)/2
= (6 + 8 + 10)/2 = 12 cm
Area of right triangle ABC = (1/2) x AB x AC
= (1/2) x 6 x 8 = 24 sq cm
We know that, area of triangle, Δ = r x s
That is 24 = r x 12
Therefore r = 2 cm