Question

In the given figure, a circle of radius 2m is inscribed in a right angled triangle of hypotenuse length 14 m, find the perimeter of the triangle?

• A. 17
• B. 32
• C. 16
• D. 34

Answer 1

The correct option is B

32

Let the circle touch the trinagle ABC at D, E and F.
Let the length of AD be x
Af =x (length of the tangents drawn from a point to the circle are equal in length).
Similarly we can say
DB =BE
FC =EC
DE =2 m (since perpendicular distance from the centre to the tangent is equal to radius)
FC =14 -x (length of the hypotenuse is 14m)
Perimeter of the triangle ABC =x+x+2+2+14-X+14-x
=32 m.