If a,b,c are the sides of a right triangle , where c is the hypotenuse. Prove that the radius r of the circle which touches the sides of the triangle is given by:`r=(a+b-c)/2`

Explanation

To prove that the radius \( r \) of the incircle of a right triangle with sides \( a \), \( b \), and hypotenuse \( c \) is given by the formula \( r = \frac{a + b - c}{2} \), we can follow these steps:

### Step 1: Understand the Triangle and the Incircle
In a right triangle, the incircle is the circle that touches all three sides of the triangle. The radius of this circle is what we need to find.

### Step 2: Use the Area of the Triangle
The area \( A \) of a right triangle can be calculated using the formula:
\[
...