Geometry Problem 1167: Triangle, Circle, Circumcircle,
Perpendicular, 90 Degrees, Collinear Points. Level: High School, Honors Geometry, College,
Mathematics Education
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D is a point on the circumcircle of a triangle ABC and E is a
point on AB (see figure below). The circumcircle of triangle ADE
cuts AC at F. If DG, DH, DM, and DN are perpendicular to BA, AC,
EF, and BC, respectively, prove that points G, H, M, and N are
collinear.
See also:
GeoGebra of problem 1167
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