Question

Let O and H be the circumcenter and orthocenter of triangle ABC, respectively. Let a, b, and c denote the side lengths, and let R denote the circumradius. Find OH^2 if R = 7 and a^2 + b^2 + c^2 = 29.

I tried to draw a diagram but it didn't work out too well. Could I have some hints plz? thanks

Answer 1

Euler's Theorem says that

OH^2 = R(R-2r) where r is the inradius

Hmmm. I'll have to think on how to figure r without knowing a,b,c...