The 80-80-20 Triangle Problem, A Variant

The isosceles triangle with the apex angle of 20° and the base angles of 80° is a recurring subject of geometric problems. The most popular is the one where cevians are drawn from the base vertices at angles of 50° and 60°, and the task is to determine one of the so formed angles.

A novel problem has been suggested by Radheyshyam Poddar:

ABC is an isosceles triangle with vertex angle ∠BAC = 20° and AB = AC. Draw ∠BCD = 60°; D lying on AB. Draw an arc with B as center and radius equal to BC. Let this arc cut AC at point E and AB at the point F. Prove that CE = DF.


  1. Solution by Mariano Perez de la Cruz
  2. Solution by Hernán Iriarte (Chile)

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