MathDB
Moving Vertex on a Triangle

Source:

March 3, 2010
conicsparabolaellipseanalytic geometryratio

Problem Statement

Given triangle ABC ABC with base AB AB fixed in length and position. As the vertex C C moves on a straight line, the intersection point of the three medians moves on: <spanclass=′latex−bold′>(A)</span> a circle<spanclass=′latex−bold′>(B)</span> a parabola<spanclass=′latex−bold′>(C)</span> an ellipse<spanclass=′latex−bold′>(D)</span> a straight line<spanclass=′latex−bold′>(E)</span> a curve here not listed <span class='latex-bold'>(A)</span>\ \text{a circle} \qquad <span class='latex-bold'>(B)</span>\ \text{a parabola} \qquad <span class='latex-bold'>(C)</span>\ \text{an ellipse} \qquad <span class='latex-bold'>(D)</span>\ \text{a straight line} \qquad <span class='latex-bold'>(E)</span>\ \text{a curve here not listed}
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