## THE NINE-POINT CIRCLE

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information

In Geometry, the Nine-Point Circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant points. They include: the midpoint of each side of the triangle, the foot of each altitude and the midpoint of the segment of each altitude from its vertex to the orthocenter (where the three altitudes meet).

The Nine-point Circle is also known as Feuerbach's Circle, Euler's Circle, Terquem's Circle, the Six-Points Circle, the Twelve-points Circle, the N-Point Circle, the Medioscribed Circle, the Mid Circle or the Circum-Midcircle.

Here are some triangle centers that lie on the Nine-Point Circle:
X(115), X(116), X(117), X(118), X(119), X(120), X(121), X(122), X(123), X(124), X(125), X(126), X(127), X(128), X(129), X(130), X(131), X(132), X(133), X(134), X(135), X(136), X(137), X(138), X(139), X(1312), X(1313), X(1560), X(1566), X(2679).

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.