MathDB
Cyclic points

Source: USAMO 1990

October 27, 2005
geometrycircumcircle

Problem Statement

An acute-angled triangle ABCABC is given in the plane. The circle with diameter  AB \, AB \, intersects altitude  CC′ \, CC' \, and its extension at points  M \, M \, and  N \, N \,, and the circle with diameter  AC \, AC \, intersects altitude  BB′ \, BB' \, and its extensions at  P \, P \, and  Q \, Q \,. Prove that the points  M,N,P,Q \, M, N, P, Q \, lie on a common circle.
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