Question

In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is ______.

Options

• 1 cm

• 2 cm

• 3 cm

• 4 cm

Answer 1

In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is 2 cm.

Explanation:

It is given that AB = 5 and BC = 12

Using Pythagoras theorem

AC² = AB² + BC²

5²+ 12²

= 169

Thus AC = 13

We know that two tangents drawn to a circle from the same point that is exterior to the circle are of equal lengths.

Thus AM = AQ = a

Similarly MB = BP = b and PC = CQ = c

We know

AB = a + b = 5

BC = b + c = 12 and

AC = a + c = 13

Solving simultaneously we get a = 3, b = 2 and c = 10

We also know that the tangent is perpendicular to the radius 

Thus OMBP is a square with side b

Hence the length of the radius of the circle inscribed in the right angled triangle is 2 cm.