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Triangles with equal areas

Source: Baltic Way 2014, Problem 13

November 11, 2014
geometrytrigonometrycircumcircletrig identitiesLaw of Sinesgeometry proposed

Problem Statement

Let ABCDABCD be a square inscribed in a circle ω\omega and let PP be a point on the shorter arc ABAB of ω\omega. Let CP∩BD=RCP\cap BD = R and DP∩AC=S.DP \cap AC = S. Show that triangles ARBARB and DSRDSR have equal areas.
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