# The 80-80-20 Triangle Problem, Solution #5

Let ABC be an isosceles triangle

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Copyright © 1996-2018 Alexander Bogomolny

This is Solution 4 from [Knop].

Let F be on AB with ∠BCF = 20°.

Then ∠BFC = 80° = ∠ABC, so that ΔBCF is isosceles and

Since also CD = BC and ∠DCF = 60°, ΔCDF is equilateral and, in particular,

ΔCEF is isosceles because ∠CEF = ∠ECF = 40°. Therefore,

### Reference

- C. Knop,
__Nine Solutions to One Problem__,*Kvant*, 1993, no 6.

### The 80-80-20 Triangle Problem

- Solution #1
- Solution #2
- Solution #3
- Solution #4
- Solution #5
- Solution #6
- Solution #7
- Solution #8
- Solution #9
- Solution #10
- Solution #11
- Solution #12

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Copyright © 1996-2018 Alexander Bogomolny

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