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equal segments wanted , 2 lines, midpoint (2016 HOMC Junior Q11)

Source:

July 20, 2019
geometryequal segments

Problem Statement

Let be given a triangle ABCABC, and let II be the midpoint of BCBC. The straight line dd passing II intersects AB,ACAB,AC at M,NM,N , respectively. The straight line d′d' (≠d\ne d) passing II intersects AB,ACAB, AC at Q,PQ, P , respectively. Suppose M,PM, P are on the same side of BCBC and MP,NQMP , NQ intersect BCBC at EE and FF, respectively. Prove that IE=IFIE = I F.
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