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perpendicular wanted, tangents on circumcircle related

Source: 2020 Dutch IMO TST 2.4

November 22, 2020
geometryperpendicular

Problem Statement

Let ABCABC be an acute-angled triangle and let PP be the intersection of the tangents at BB and CC of the circumscribed circle of △ABC\vartriangle ABC. The line through AA perpendicular on ABAB and cuts the line perpendicular on ACAC through CC at XX. The line through AA perpendicular on ACAC cuts the line perpendicular on ABAB through BB at YY. Show that AP⊥XYAP \perp XY.
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