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Area of the Triangle

Source: 1966 AHSME #38

August 31, 2011
geometryAMC

Problem Statement

In triangle ABCABC the medians AMAM and CNCN to sides BCBC and ABAB, respectively, intersect in point OO. PP is the midpoint of side ACAC, and MPMP intersects CNCN in QQ. If the area of triangle OMQOMQ is nn, then the area of triangle ABCABC is:
(A) 16n(B) 18n(C) 21n(D) 24n(E) 27n\text{(A)}\ 16n\qquad \text{(B)}\ 18n\qquad \text{(C)}\ 21n\qquad \text{(D)}\ 24n\qquad \text{(E)}\ 27n
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