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
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