Spieker circle

In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker.

[1] The Spieker center is also the point where all three cleavers of the triangle (perimeter bisectors with an endpoint at a side's midpoint) intersect each other.

In 1862, he published Lehrbuch der ebenen geometrie mit übungsaufgaben für höhere lehranstalten, dealing with planar geometry.

Due to this publication, influential in the lives of many famous scientists and mathematicians including Albert Einstein, Spieker became the mathematician for whom the Spieker circle and center were named.

The incenter of the triangle and the Nagel point form a line within the Spieker circle.

[2] The nine-point circle with the Euler line and the Spieker circle with the Nagel line are analogous to each other, but are not duals, only having dual-like similarities.