(AN) is touches to (K,KB) and (L,LC)
Source: Oral Moscow Geometry Olympiad 2024, 10-11.6
September 3, 2024
geometry
Problem Statement
An unequal acute-angled triangle with an orthocenter is given, is the midpoint of side . Points and lie on a line passing through and perpendicular to such a and perpendicular to . Point lies on the line , and the lines and are symmetric with respect to the line . Prove that a circle with a diameter touches two circles: centered at and with a radius and with a center and radius .