Question

abc is a right triangle right angled at b such that bc=6cm and ab=8cm find the radius of the circle

Answer 1

Question is about  the radius of Incircle or Circumcircle.

ΔABC is a right angle triangle. ∠B = 90°.
AB = 8 cm.     BC = 6 cm.    

Using Pythagoras theorem we get   AC² = AB² + BC² = 100
=> AC = 10 cm
=> Radius of circumcircle = R = 1/2 * Hypotenuse = 5 cm

s = semiperimeter = (a+b+c)/2 = 12 cm
r = incircle radius
Ar(ΔABC) = 1/2 * AB * BC = 24 cm²
                 = s * r
                 = 12 * r

=>  r = incircle radius = 24/12 = 2 cm.

Answer 2

r of inner circle=24/12 =2cm...

hope it helps....