Consider a triangle ABC in which A+ B+ C= 3 3 What is the value of A 2 B 2 C 2 ?

Step-by-step solution

aligned & Given A+ B+ C= 3 3 & A+ B+ C & =2 A+B 2 A-B 2 + (1-2 ^2 C 2 ) & =2 C 2 A-B 2 +1-2 ^2 C 2 ( A+B 2 =90^ - C 2 ) & =1+2 C 2 [ A-B 2 - C 2 ] & =1+2 C 2 [ A-B 2 - A+B 2 ] & =1+4 C 2 A 2 B 2 & A+ B+ C= 3 3 & 1+4 C 2 A 2 B 2 = 3 3 aligned aligned & 1+4 C 2 A 2 B 2 = 3 3 2 & 4 A 2 B 2 C 2 = 3 2 -1 aligned A 2 B 2 C 2 = 1 8