MathDB

2009.89.5

Part of Kyiv City MO Juniors 2003+ geometry

Problems(1)

orthocenter, perpendicular chords, AP = 2PB (Kyiv City Olympiad 2009 8.5 9.3)

Source:

7/2/2020
A chord ABAB is drawn in the circle, on which the point PP is selected in such a way that AP=2PBAP = 2PB. The chord DEDE is perpendicular to the chord ABAB and passes through the point PP. Prove that the midpoint of the segment APAP is the orthocener of the triangle AEDAED.
geometryChordsorthocentercircle