If , and are length of the altitudes of a A B C with area , then ^2 R^2 ( 1 ^2 + 1 ^2 + 1 ^2 ) is equal to

Step-by-step solution

Area of triangle = 1 2 base altitude = 1 2 a = 1 2 b = 1 2 c = 2 a , = 2 b and = 2 c ^2 R^2 ( 1 ^2 + 1 ^2 + 1 ^2 )= ^2 R^2 ( a^2 4 ^2 + b^2 4 ^2 + c^2 4 ^2 ) aligned & = 1 4 R^2 (4 R^2 ^2 A+4 R^2 ^2 B+4 R^2 ^2 C ) & [ A a = B b = C c = 1 2 R ] & = ^2 A+ ^2 B+ ^2 C aligned