​a, b and c are the sides of a right triangle with c as hypotenuse. The radius r, of the circle which touches the three sides of the triangle is :

Correct option is B

Given:

A right-angled triangle with sides a, b and hypotenuse c.

The radius r of the incircle is to be determined.

Formula Used:

The inradius of a right-angled triangle is given by:

r =  $$\frac{\text{Area of the triangle}}{\text{Semi-perimeter}} ​$$​​

Solution:

The semi-perimeter of the triangle:

s = $$\frac{a + b + c}{2}$$​​

The area of the right triangle:

A = $$\frac{1}{2} \times a \times b$$

The inradius formula simplifies to:

r = $$\frac{a + b - c}{2}​$$

Option (B) is right.