APMO 1991 Q1: Upper Secondary Mathematics Competition Question

Let G be the centroid of triangle ABC and M be the midpoint of BC. Let X be on AB and Y on AC such that the points X, Y and G are collinear and XY and BC are parallel.

Suppose that XC and GB intersect at Q and YB and GC intersect at P. Show that triangle MPQ is similar to triangle ABC.


[APMO 1991 Q1]

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