MathDB
Collinearity

Source: China TST 2004 Quiz

February 1, 2009
geometryincenterperimetergeometric transformationreflectiongeometry unsolved

Problem Statement

Two equal-radii circles with centres O1 O_1 and O2 O_2 intersect each other at P P and Q Q, O O is the midpoint of the common chord PQ PQ. Two lines AB AB and CD CD are drawn through P P ( AB AB and CD CD are not coincide with PQ PQ ) such that A A and C C lie on circle O1 O_1 and B B and D D lie on circle O2 O_2. M M and N N are the mipoints of segments AD AD and BC BC respectively. Knowing that O1 O_1 and O2 O_2 are not in the common part of the two circles, and M M, N N are not coincide with O O. Prove that M M, N N, O O are collinear.
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