Steiner ellipses

Given any triangle, there are two special ellipses called the Steiner inellipse and the Steiner circumellipse. The Steiner inellipse is the unique ellipse that is tangent to the sides of the triangle at their midpoints. The Steiner circumellipse is the unique ellipse that passes through the triangle's vertices and has its center at the triangle's centroid.

Important properties

• The Steiner inellipse is tangent to the sides of the triangle at the midpoints.

• The Steiner circumellipse passes through all three vertices of the triangle.

• Both ellipses have their centers at the centroid of the triangle.

• The axes of the Steiner ellipses are related to the geometry of the triangle.