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equal angles wanted, circumcircle, perpendiculars and orthocenter related

Source: Singapore Open Round 2 , 2019

July 12, 2019
geometrycircumcircleorthocenterequal angles

Problem Statement

In the acute-angled triangle ABCABC with circumcircle ω\omega and orthocenter HH, points DD and EE are the feet of the perpendiculars from AA onto BCBC and from BB onto ACAC respecively. Let PP be a point on the minor arc BCBC of ω\omega . Points MM and NN are the feet of the perpendiculars from PP onto lines BCBC and ACAC respectively. Let PHPH and MNMN intersect at RR. Prove that ∠DMR=∠MDR\angle DMR=\angle MDR.
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