If r and R are radii of the incircle and circumcircle of triangle ABC, prove that 8rR(cos^2 A/2 + cos^2 B/2 + cos^2 C/2) = 2bc + 2ca + 2ab - a^2 - b^2 - c^2.

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- July 24th 2008, 06:16 AMfardeen_genQuestion involving properties of triangles and trigonometry?
If r and R are radii of the incircle and circumcircle of triangle ABC, prove that 8rR(cos^2 A/2 + cos^2 B/2 + cos^2 C/2) = 2bc + 2ca + 2ab - a^2 - b^2 - c^2.