Problem 21: Acute Triangle, Orthocenter, Circle, Diameter, Tangent, Collinear Points. Level: High School, College, Math Education.

The drawing shows an acute triangle ABC with the orthocenter H. The tangents from A to the circle with diameter BC touch the circle at M and N. Prove that M, H, N are collinear (passing through the same straight line).
 



 

 

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Online education degree: geometry problems 21-30

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Geometry Jobs

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."
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