## The 80-80-20 Triangle Problem, A Derivative, Solution #2

ABC is an isosceles triangle with vertex angle

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Copyright © 1996-2018 Alexander Bogomolny

The solution is by Ian McGee of the University of Waterloo [Honsberger]. It was also found independently by Aditi Khetwal, a student of John Rhodes at the Woodhouse College, London, UK.

Construct an isosceles triangle AEQ with ∠AQE = 20°. Since.

∠CAQ = ∠EAQ - ∠EAC = 80° - 20° = 60°.

Which makes ΔACQ equilateral. In particular,

In ΔCQE, EQ = CQ and

### Reference

- R. Honsberger,
*Mathematical Chestnuts from Around the World*, MAA, 2001, Ch 2.

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Copyright © 1996-2018 Alexander Bogomolny