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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.
  

Elearning Geometry Problem 1167: Triangle, Circle, Circumcircle, Perpendicular, 90 Degrees, Collinear Points

 

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GeoGebra of problem 1167
 


 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | Problems Art Gallery | Art | 1161-1170 | Triangle | Circle | Intersecting Circles | Circumcircle | 90 degrees | Collinear Points | Simson Line | Email | by Antonio Gutierrez

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Last updated: Nov 19, 2015