If A B C is right angled at A , then r₂+r₃ is equal to

Step-by-step solution

Given that A=90^ Now, r₂+r₃=4 R A 2 B 2 C 2 +4 R A 2 aligned & =4 R A 2 [ B 2 C 2 + B 2 C 2 ] & =4 R 45^ ( B+C 2 ) & =4 R B 2 C 2 ( 2 - A 2 ) & =4 R 1 2 ( A 2 ) & =4 R 1 2 45^ & =4 R 1 2 1 2 =2 R r₂ & +r₃=2 R aligned Also, aligned Also, & & r₁+r₂+r₃-r=4 R=2(2 R) & & r₁+r₂+r₃-r=2 (r₂+r₃ ) & & r₂+r₃=r₁-r aligned