IMO 1971 LL BUL7

In a triangle ABC, let H be its orthocenter, O its circumcenter,

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IMO 1971 LL BUL7

Origin: BUL

Problem

In a triangle ABC, let H be its orthocenter, O its circumcenter, and R its circumradius. Prove that: (a) |OH| = R\sqrt1 −8 cos \alpha cos \beta cos \gamma, where \alpha, \beta, \gamma are angles of the tri- angle ABC; (b) O \equivH if and only if ABC is equilateral.