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IMOC 2017 G1 (MT // angle bisector, BP = CQ)

Source: https://artofproblemsolving.com/community/c6h1740077p11309077

March 20, 2020
geometryangle bisector

Problem Statement

Given △ABC\vartriangle ABC. Choose two points P,QP, Q on AB,ACAB, AC such that BP=CQBP = CQ. Let M,TM, T be the midpoints of BC,PQBC, PQ. Show that MTMT is parallel to the angle bisevtor of ∠BAC\angle BAC http://4.bp.blogspot.com/-MgMtdnPtq1c/XnSHHFl1LDI/AAAAAAAALdY/8g8541DnyGo_Gqd19-7bMBpVRFhbXeYPACK4BGAYYCw/s1600/imoc2017%2Bg1.png
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