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Projection of M onto the line l is on PK

Source: Baltic Way 2009

November 27, 2010
geometrygeometric transformationhomothetyangle bisectorgeometry proposed

Problem Statement

Let MM be the midpoint of the side ACAC of a triangle ABCABC, and let KK be a point on the ray BABA beyond AA. The line KMKM intersects the side BCBC at the point LL. PPis the point on the segment BMBM such that PMPM is the bisector of the angle LPKLPK. The line ℓ\ell passes through AA and is parallel to BMBM. Prove that the projection of the point MM onto the line ℓ\ell belongs to the line PKPK.
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