Question

A circle is drawn inside a right angle triangle whose sides are a,b,c where c is hyotenuse.touches all side of circle.prove that r=a+b-c/2

Answer 1

Answer:

Step-by-step explanation: see

Answer 2

Answer:

r = (a + b + c)/2

Step-by-step explanation:

Find the attached picture for explanation of the problem & solution.  

The circle is inscribed inside the triangle. The circle is touching all three sides of the right angle triangle.  

BC = a, AC = b, AB = c

AE and AF are tangetns drawn to circle from external point A

Hence AE = AF.

Similarly, we can say BD = BF and CE = CD

The radius of the inside circle is shown by OE = OD = OF = r

The quadrilateral OECD is a square as OE = OD and CD = CE and angles are 90 degrees.

AF = b – r

BF = a – r

AB = c = AF + FB = b – r + a – r

Hence r = (a + b + c)/2