Online Geometry Problems, High School, College

Geometry Problem 729: Triangle, Altitude, Orthocenter, Circumcircle, Perpendicular, Midpoint. Level: High School, Honors Geometry, College, Mathematics Education

Geometry problems 721-730

The diagram shows a triangle ABC with the orthocenter H and the circumcircle O. D is a point on the arc BC, DE is perpendicular to AB, and DF is perpendicular to BC. DH meets EF at M. Prove that M is the midpoint of DH.
 

 Triangle, Orthocenter, Circumcircle, Perpendicular, Midpoint

 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 721-730 | Triangles | OrthocenterCircles | Circumcircle | Altitude | Perpendicular lines | Midpoint | Email | Solution / comment | By Antonio Gutierrez