WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

The Hagge Circle

​
Let ABC be a triangle and H its orthocenter. Let P be a point and AP, BP, and CP meet the circumcircle of ABC again at A', B', and C'. Let A'', B'', and C'' be the reflections of A', B', and C' about BC, AC, and AB. Let A''P, B''P, and C''P intersect AH, BH, and CH at X, Y, and Z. Then H, A'', B'', C'', X, Y, and Z are concyclic.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.