## The 80-80-20 Triangle Problem, 60-70 Variant, Solution #2

Let ABC be an isosceles triangle |

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Copyright © 1996-2017 Alexander Bogomolny

The solution is by Radu Ionescu.

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

Let O be the intersection of BD and CE and H the intersection of BD and CF. Since

∠FBO = ∠FCO = 20°, |

quadrilateral BCOF is cyclic. In particular,

∠OFC = ∠ OBC = 60°. |

From the classical problem, ∠CFD = 80° which implies that

In ΔDFH, ∠HFD = (∠CFD) = 80°.

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