MathDB
Equal Areas in a Triangle

Source:

June 8, 2009
geometryratiocircumcircle

Problem Statement

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: <spanclass=latexbold>(A)</span> the center of the inscribed circle<spanclass=latexbold>(B)</span> the center of the circumscribed circle<spanclass=latexbold>(C)</span> such that the three angles fromed at the point each be 120<spanclass=latexbold>(D)</span> the intersection of the altitudes of the triangle<spanclass=latexbold>(E)</span> the intersection of the medians of the triangle <span class='latex-bold'>(A)</span>\ \text{the center of the inscribed circle} \qquad \\ <span class='latex-bold'>(B)</span>\ \text{the center of the circumscribed circle}\qquad \\ <span class='latex-bold'>(C)</span>\ \text{such that the three angles fromed at the point each be }{120^\circ}\qquad \\ <span class='latex-bold'>(D)</span>\ \text{the intersection of the altitudes of the triangle}\qquad \\ <span class='latex-bold'>(E)</span>\ \text{the intersection of the medians of the triangle}