IMO 1988 LL SPA75

Let ABC be a triangle with inradius r and circumradius R.

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IMO 1988 LL SPA75

Origin: SPA

Problem

Let ABC be a triangle with inradius r and circumradius R. Show that sin A 2 sin B 2 + sin B 2 sin C 2 + sin C 2 sin A 2 \leq5 8 + r 4R.