4 Point Circle

This triangle contains four different special points, defined by the triangle.

These points are: intersection of angular bisectors (red lines, point H),

intersection of altitudes (purple lines, point K), intersection of perpendicular

bisectors (green lines, point F), and intersection of the lines joining

verticies with the midpoints opposite them (blue lines, point G)

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Distance from G to KF
Distance from H to KF

Three of the four points are always collinear.

 Is the other point ever collinear?

If so, in what cases is it collinear?

App generated by Geometry Expressions