Geometry Problem 1442: Unlocking Triangular Altitude Intersection (Orthocenter): Discover the Secrets of Congruent Angles and Intersecting Lines!

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

 

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

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Illustrating Problem 1442: A Creative Poster Using iPad Apps

Poster of Geometry Problem 1442: Triangle, Altitudes, Orthocenter, Perpendicular, Congruent Angles, Similarity, Measurement, iPad Apps, Typography. Math Infographic, Tutor

Explore More: Art of Problem 1442 with Generative Sketching Techniques!.

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.


Geometry Problem 1442 Solution(s)