1957 AHSME Problem 26

From a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be:

\begin{array}{l} \textbf{(A)}\ \text{the center of the inscribed circle} \qquad \\ \textbf{(B)}\ \text{the center of the circumscribed circle}\qquad\\ \textbf{(C)}\ \text{such that the three angles formed at the point each be }{120^\circ}\qquad\\ \textbf{(D)}\ \text{the intersection of the altitudes of the triangle}\qquad\\ \textbf{(E)}\ \text{the intersection of the medians of the triangle} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.