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Altitudes and circles

Source: Austrian MO 2005 round 2

June 27, 2005
geometryAustriaAUT

Problem Statement

Triangle DEFDEF is acute. Circle c1c_1 is drawn with DFDF as its diameter and circle c2c_2 is drawn with DEDE as its diameter. Points YY and ZZ are on DFDF and DEDE respectively so that EYEY and FZFZ are altitudes of triangle DEFDEF . EYEY intersects c1c_1 at PP, and FZFZ intersects c2c_2 at QQ. EYEY extended intersects c1c_1 at RR, and FZFZ extended intersects c2c_2 at SS. Prove that PP, QQ, RR, and SS are concyclic points.
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