An Incredible Ratio
Given a triangle , an ellipse is drawn through the points such that it's center is at the centeroid of the triangle. Another ellipse is drawn through the mid points of touching these line segments.
What is the ratio of the area of the later ellipse to that of the former?
The answer is 0.25.
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1 solution
The ellipses are known as Steiner Circumellipse and Steiner Inellipse . Using the well known properties linking their areas with the triangle's we arrive at the answer 4 1