Altitudes of a triangle meet at orthocenter. Midsegment and line through vertex and orthocenter 90 d

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Question: Altitudes AD,CF of the triangle ABC meet at H. X,Z,P are the midpoints of AB,AC,CH respectively. Prove that angle XZP is a right angle
This is a geometry problem out of the book "A course in Geometry Plain and Solid" by Arthur Weeks and Jackson Adkins

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