If in a A B C, r₃=r₁+r₂+r , then A+ B is equal to

Step-by-step solution

We know that, aligned & r=4 R A 2 B 2 C 2 & r₁=4 R A 2 B 2 C 2 & r₂=4 R B 2 A 2 C 2 & r₃=4 R C 2 A 2 B 2 aligned Given that, aligned & r₃=r₁+r₂+r & r₃-r=r₁+r₂ & 4 R C 2 ( A 2 B 2 - B 2 A 2 ) & =4 R C 2 [ A 2 B 2 + A 2 B 2 ] & C 2 ( ( A+B 2 ) )= C 2 ( ( A+B 2 ) ) & C 2 ( ( 2 - C 2 ) )= C 2 ( ( 2 - C 2 ) ) & [ A+B+C= A 2 + B 2 = 2 -C ] & ^2 A 2 = ^2 C 2 & C 2 =1 & aligned C 2 = 4 C= 2 We know that, A+B+C= array ll & A+B= - 2 & A+B= 2 array