MathDB
Collinear

Source: Chinese TST

April 6, 2008
geometrycircumcircleincentergeometric transformationreflectionratiotrigonometry

Problem Statement

Let ABC ABC be an acute triangle, let M,N M,N be the midpoints of minor arcs CA^,AB^ \widehat{CA},\widehat{AB} of the circumcircle of triangle ABC, ABC, point D D is the midpoint of segment MN, MN, point G G lies on minor arc BC^. \widehat{BC}. Denote by I,I1,I2 I,I_{1},I_{2} the incenters of triangle ABC,ABG,ACG ABC,ABG,ACG respectively.Let P P be the second intersection of the circumcircle of triangle GI1I2 GI_{1}I_{2} with the circumcircle of triangle ABC. ABC. Prove that three points D,I,P D,I,P are collinear.
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