## The 80-80-20 Triangle Problem, 60-70 Variant, Solution #1

Let ABC be an isosceles triangle |

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Copyright © 1996-2018 Alexander Bogomolny

The solution is by Philippe Fondanaiche.

Find F on AB with ∠BCF = 50°. This brings us into the classical framework so that we, for example, know that

In ΔBDF, ∠DBF = 20° and

(1) | DF / EF = BF / CF |

Since ∠BFC = 50°, ΔBCF is isosceles and

∠CED = ∠DEF - ∠CEF = 50° - 30° = 20°. |

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Copyright © 1996-2018 Alexander Bogomolny