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Compute the area of the concave quadrilateral ABHC

Source: Greek National Mathematical Olympiad 2008 - P3

November 17, 2011
geometrytrigonometrygeometry unsolved

Problem Statement

A triangle ABCABC with orthocenter HH is inscribed in a circle with center KK and radius 11, where the angles at BB and CC are non-obtuse. If the lines HKHK and BCBC meet at point SS such that SK(SKāˆ’SH)=1SK(SK -SH) = 1, compute the area of the concave quadrilateral ABHCABHC.
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