Geometry Problem 1361: Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps.

Proposition

The figure below shows a triangle ABC. Circle of diameter AC intersects AB and BC at D and E, respectively. C₁ is the nine-point circle of triangle ABC and C₂ is the nine-point circle of triangle DBE. Circles C₁ and C₂ intersect at F and G. Prove that the angles DBG and EBF are congruent.
 

See solution below

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Sketch and Typography of problem 1361 using iPad Apps

See solution below

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