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collinear wanted , 3 altitudes related

Source: XIV Kyiv Tournament of Mathematical Battles named after Lesya Rublev 2017, Team Oral Olympiad Middle p5

June 2, 2022
collinearaltitudesgeometryKyiv Tournament

Problem Statement

Let AD AD , BE BE and CF CF be the altitudes of ΔABC \Delta ABC . The points P,  Q,  R P, \, \, Q, \, \, R and S S are the feet of the perpendiculars drawn from the point D D on the segments BA BA , BE BE , CF CF and CA CA , respectively. Prove that the points P,  Q,  R P, \, \, Q, \, \, R and S S are collinear.
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