In A B C , if 4 r₁=5 r₂=6 r₃ , then ^2 A 2 + ^2 B 2 + ^2 C 2 =

Step-by-step solution

We know that aligned & r₁= s-a , r₂= s-b and r₃= s-c & 4 r₁=5 r₂=6 r₃ & 4 s-a = 5 s-b = 6 s-c 4 s-a = 5 s-b = 6 s-c = 1 k ( say ) & s-a=4 k, s-b=5 k, s-c=6 k & Now, s-a+s-b+s-c=15 k & 3 ~s -(a+b+c)=15 k & 3 ~s -2 ~s =15 k ~s =15 k & 15 k-a=4 k a=11 k & Similarly, b=10 k, c=9 k & Now, ^2 ~A 2 + ^2 ~B 2 + ^2 C 2 & (s-b)(s-c) b c + (s-a)(s-c) c a + (s-a)(s-b) a b & = 30 k^2 90 k^2 + 24 k^2 59 k^2 + 20 k^2 110 k^2 = 1 3 + 8 33 + 2 11 = 25 33 aligned