Question

ABC is a right angles triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.

Calculate the value of x, the radius of the inscribed circle.

Answer 1

In ΔABC, ∠B = 90°

OL ⊥ AB, OM ⊥ BC and ON ⊥ AC 

LBNO is a square

LB = BN = OL = OM = ON = x

∴ AL = 12 – x 

∴ AL = AN = 12 – x 

Since ABC is a right triangle

AC² = AB² + BC²

`=>` 13² = 12² + BC²

`=>` 169 = 144 + BC²

`=>` BC² = 25

`=>` BC = 5

∴ MC = 5 – x

But CM = CN

∴ CN = 5 – x

Now, AC = AN + NC

13 = (12 – x) + (5 – x)

13 = 17 – 2x

2x = 4

x = 2 cm