Geometry Problems, Online Education

Problem 546: Triangle, Angle Trisectors, 60 Degrees, Equilateral triangle. Level: High School, SAT Prep, College

The figure shows a triangle ABC with AD and AE trisectors of angle BAC (angles BAD=DAE=EAC=a), and CE and CF trisectors of angle ACB (angles ACE=ECF=FCB=c). If angle AED=60+c, and angle CEF=60+a, prove that the triangle DEF is an equilateral triangle.

Triangle, Angle Trisectors, Equilateral triangle, 60 degrees

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