Question

Q4. Solve any two of the following questions:
A circle with centre "O is incircle of triangleABC. angle ACB = 90°.
Radius of the circle is r
Prove that:2r = a +b-c​

Answer 1

Answer is :-

The circle touches the sides BC, CA, AB of the righ triangle ABC at D, E and F respectively.

Assume BC = a, CA = b and AB = c

Then, AE = AF and BD = BF and CE = CD.

OE = OD = OF = r.

Here OEDC is a square then CE = CD = r.

i.e., b - r = AF, a - r = BF or AB = c = AF + BF = b - r + a - r

Therefore, r = (a + b - c)/2

2r = a + b - c