Question

pls anyone answer ques 15

Answer 1

ABC is right angle triangle.
so, a^2+b^2=c^2
(a+b)^2-2ab=c^2
(a+b)^2-c^2=2ab
(a+b-c)(a+b+c)=2ab -----------(1)


let r is the radius of circle .

1/2 x r x (a+b+c)=(1/2) x ab
r=ab/(a+b+c)
from equation (1)
r=(a+b+c)(a+b-c)/2 (a+b+c)
=(a+b-c)/2

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