Properties
The medial triangle can also be viewed as the image of triangle ABC transformed by a homothety centered at the centroid with ratio -1/2. Hence, the medial triangle is inversely similar and shares the same centroid and medians with triangle ABC. It also follows from this that the perimeter of the medial triangle equals the semiperimeter of triangle ABC, and that the area is one quarter of the area of triangle ABC.
Note that the orthocenter of the medial triangle coincides with the circumcenter of triangle ABC. This fact provides a tool for proving collinearity of the circumcenter, centroid and orthocenter. The medial triangle is the pedal triangle of the circumcenter.
A point in the interior of a triangle is the center of an inellipse of the triangle if and only if the point lies in the interior of the medial triangle.
Read more about this topic: Medial Triangle
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