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center of ellipse through midpoints of triangle 2017 BMT Individual 19

Source:

January 3, 2022
conicsellipsegeometryanalytic geometry

Problem Statement

Let TT be the triangle in the xyxy-plane with vertices (0,0)(0, 0), (3,0)(3, 0), and (0,32)\left(0, \frac32\right). Let EE be the ellipse inscribed in TT which meets each side of TT at its midpoint. Find the distance from the center of EE to (0,0)(0, 0).
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