MathDB

6.3

Part of MathLinks Contest 7th

Problems(1)

0763

Source:

6/23/2008
Let Ω \Omega be the circumcircle of triangle ABC ABC. Let D D be the point at which the incircle of ABC ABC touches its side BC BC. Let M M be the point on Ω \Omega such that the line AM AM is parallel to BC BC. Also, let P P be the point at which the circle tangent to the segments AB AB and AC AC and to the circle Ω \Omega touches Ω \Omega. Prove that the points P P, D D, M M are collinear.
geometrycircumcirclegeometric transformationhomothetylinear algebramatrixincenter