KN bisects CM, diameter , perpendiculars related (2013 Kyiv City MO 11.3)
Source:
August 4, 2020
geometrybisects segmentdiameterperpendicular
Problem Statement
The segment is the diameter of the circle. The points and belong to this circle and are located in different half-planes relative to the line . From the point the perpendiculars and are drawn on the lines and , respectively. Prove that the line intersects the segment in its midpoint.(Igor Nagel)