MathDB
Geometry warmup: internally tangent circles

Source: HMMT Invitational Contest 2016, Problem 2

April 22, 2016
geometryHMMTHMICHi

Problem Statement

Let ABCABC be an acute triangle with circumcenter OO, orthocenter HH, and circumcircle Ω\Omega. Let MM be the midpoint of AHAH and NN the midpoint of BHBH. Assume the points MM, NN, OO, HH are distinct and lie on a circle ω\omega. Prove that the circles ω\omega and Ω\Omega are internally tangent to each other.
Dhroova Aiylam and Evan Chen
Back to ProblemsView on AoPS