Sliced Triangle Areas
Medians AD and BE of triangle ABC intersect at P . A line through P parallel to AB meets AC and BC at M and N , respectively. The ratio of the area of MNC to the area of ABC can be written as , where m and n are positive coprime integers. Find .
The answer is 13.
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MPN is parallel to AB, and P is the centroid of triangle ABC: CP intersects AB at F, the midpoint of AB. It is known that CP/PF=2: The medians divide the centroid in a 2:1 ratio. So triangle CMN is similar to CAB with ratio 2:3, so the ratio of their areas is 4/9. 4+9=13.