MathDB
Concyclic Points - Switzerland 2011

Source:

March 22, 2011
geometryparallelogramratiosimilar trianglespower of a pointgeometry proposed

Problem Statement

Let ABCDABCD be a parallelogram and HH the Orthocentre of △ABC\triangle{ABC}. The line parallel to ABAB through HH intersects BCBC at PP and ADAD at QQ while the line parallel to BCBC through HH intersects ABAB at RR and CDCD at SS. Show that PP, QQ, RR and SS are concyclic.
(Swiss Mathematical Olympiad 2011, Final round, problem 8)
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