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AREA in terms of S.

Source: JBMO 2014, pr 2

June 23, 2014
geometryanalytic geometryparallelogramcircumcircle

Problem Statement

Consider an acute triangle ABCABC of area SS. Let CD⊥ABCD \perp AB (D∈ABD \in AB), DM⊥ACDM \perp AC (M∈ACM \in AC) and DN⊥BCDN \perp BC (N∈BCN \in BC). Denote by H1H_1 and H2H_2 the orthocentres of the triangles MNCMNC, respectively MNDMND. Find the area of the quadrilateral AH1BH2AH_1BH_2 in terms of SS.
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