Question

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

Answer 1

Ans: By Pythagoras theorem,

BC^2 = AB^2 + AC^2
BC^2 = 64 + 36
BC = 10 cm

let O be centre .

In triangle AOB
area = 1/2 × 6 × r
= 3r

In triangle AOC
area = 1/2 × 8 × r
= 4r

In triangle AOB
area = 1/2 × 10 × r
= 5r

Area of triangle ABC = 3r + 4r + 5r
1/2 × 6 × 8 = 12r
24 = 12r
r = 2cm

Hope it helps...!!