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AC is tangent to circumcircle of DEF (HOMC 2018 ind. sen12)

Source:

February 2, 2020
geometrycircumcircletangentparallelaltitudes

Problem Statement

Let ABCABC be an acute triangle with AB<ACAB < AC, and let BEBE and CFCF be the altitudes. Let the median AMAM intersect BEBE at point PP, and let line CPCP intersect ABAB at point DD (see Figure 2). Prove that DE∥BCDE \parallel BC, and ACAC is tangent to the circumcircle of △DEF\vartriangle DEF. https://cdn.artofproblemsolving.com/attachments/f/7/bbad9f6019a77c6aa46c3a821857f06233cb93.png
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