medial triangle

The medial triangle of a triangle $\mathrm{△}ABC$ is the triangle formed by joining the midpoints of the sides of the triangle $\mathrm{△}ABC.$

Here, $\mathrm{△}{A}^{\prime }{B}^{\prime }{C}^{\prime }$ is the medial triangle. The incircle of the medial triangle is called the Spieker circle and the incenter is called the Spieker center. The circumcircle of the medial triangle is called the medial circle.

An important property of the medial triangle is that the medial triangle $\mathrm{△}{A}^{\prime }{B}^{\prime }{C}^{\prime }$ of the medial triangle $\mathrm{△}DEF$ of $\mathrm{△}ABC$ is similar to $\mathrm{△}ABC.$

Title	medial triangle
Canonical name	MedialTriangle
Date of creation	2013-03-22 13:11:17
Last modified on	2013-03-22 13:11:17
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	8
Author	yark (2760)
Entry type	Definition
Classification	msc 51-00
Synonym	auxiliary triangle
Defines	Spieker center
Defines	Spieker circle
Defines	medial circle