MathDB
KN bisects CM, diameter , perpendiculars related (2013 Kyiv City MO 11.3)

Source:

August 4, 2020
geometrybisects segmentdiameterperpendicular

Problem Statement

The segment ABAB is the diameter of the circle. The points MM and CC belong to this circle and are located in different half-planes relative to the line ABAB. From the point MM the perpendiculars MNMN and MKMK are drawn on the lines ABAB and ACAC, respectively. Prove that the line KNKN intersects the segment CMCM in its midpoint.
(Igor Nagel)