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Three Perps (Posted on 2010-06-11) Difficulty: 2 of 5

Let ABC be an equilateral triangle with K its circumcircle.

Let P be a point on K (different from A, B, and C) and m 
the tangent line to K at point P.

Let D, E, and F be points on m such that AD, BE, and CF 
are perpendicular to m.

Prove that |AD| + |BE| + |CF| equals twice the length of 
an altitude of triangle ABC.

See The Solution Submitted by Bractals    
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  Subject Author Date
Some ThoughtsMechanics ApproachHarry2010-06-11 20:07:47
Analytic solutionJer2010-06-11 16:01:23
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