Geometry Problem 1442: Triangle, Altitudes, Orthocenter, Perpendicular, Congruent Angles, Similarity, Measurement

In the figure below, the altitudes AD and CE of triangle ABC meet at F, BF meets DE at G so that angles BAC and ACG are congruent. BH is perpendicular to DE and CG extended meets BH at M. If CG = 3 and GM = 2, find BM.

See solution below

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Poster of Problem 1442 using iPad Apps

See also:
Art of problem 1442, Generative Sketching.

Geometric Art using iPad or Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.