Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 980.

## Thursday, February 13, 2014

### Geometry Problem 980. Equilateral Triangle, Vertices, Three Parallel, Equal Circles, Construction

Labels:
circle,
construction,
equilateral,
parallel,
triangle,
vertex

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Because AC//DF and BD//CE, 60=<BOC=<BDF, 60=<AOQ=180-<ACF=<DFC, then <DFC=<BDF so OCDF is cyclic isosceles trapezoid. But 60=180-<QOD=<ECF so <DFC=<ECF which makes FEDC isosceles trapezoid as well. That means DEOCF is cyclic and OEF equilateral from subtended angles.

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