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Geometry Problem 1113: Triangle, Perpendicular Bisector, 90 Degrees, Circle, Concyclic Points, Cyclic Quadrilateral. Level: High School, SAT Prep, College, Mathematics Education

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The figure shows a triangle ABC. MD is the perpendicular bisector of AC (D on BC) and NE is the perpendicular bisector of BC (E on CA). MD and NE meet at O. Prove that (1) CO and DE are perpendicular; (2) Points E, A, O, D, and B are concyclic.
 

Infographic Geometry problem 1113: Triangle, Perpendicular Bisector, 90 Degrees, Circle, Concyclic Points, Cyclic Quadrilateral
 

 

"There is geometry in the humming of the strings. There is music in the spacing of the spheres."
 Pythagoras. ca.560-ca.480 BC.
 

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Last updated: Apr 27, 2015 by Antonio Gutierrez.