Question

If r1 = r2 + r3 +r show that the triangle is a right angle triangle

Answer 1

r1=6r by using a property 1/r1+1/r2+1/r3=1/rAs,r1=stanA/2, r=(s-a)tanA/2 ,So,s/(s-a)=6a=5s/6Similarly,b=2s/3,c=s/2,So,triangle is right angled at A

Answer 2

If $r_{1} = r_{2} +  r_{3} + r$ then the triangle is a right angled triangle.

Let ABC be a triangle.

 AB = c

 BC = a

 CA = b

To prove ABC is a right triangle, we need to prove

  $a^{2} = b^{2} + c^{2}$

Please refer attachment