Home Geometry Problems All Problems Isosceles Triangle 80-20-80 351-360 View or post a solution 
Problem 358. Isosceles triangle 80-80-20, Circle, Angles, Congruence.
Level: High School, College, SAT Prep.

In the figure below, triangle ABC is isosceles with AB = BC and angle B = 20. The cevian AD is equal to BD and the circle of center C and radius equal to CA cut AB and BC at points E and F, respectively.
Prove that AE = DF. Try to use elementary geometry (Euclid's Elements.)

Isosceles triangle 80-80-20 



Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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