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Topic: Euclidean problem
Replies: 1   Last Post: Mar 31, 2014 10:44 AM

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Peter Scales

Posts: 192
From: Australia
Registered: 4/3/05
Re: Euclidean problem
Posted: Mar 31, 2014 10:44 AM
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> Hi,
> I've some troubles trying to prove this problem:
> Given a square (ABCD) , E is an internal point to the
> square such that the angle ECD = angle EDC = 15°;
> prove that ABE is an equilateral triangle.
> I've just managed to prove that ABE is isosceles, but
> can't move forward. Hope someone can help me figure
> out the right path!

Hi GabMat,
Bisect the square (side=a) with line FEG, F on CD, G on AB
Let EF=h=(a/2)*tan15deg=(a/2)*(2-sqrt(3))
: EG=a-h=a-(a/2)*(2-sqrt(3))=(a/2)*sqrt(3)
In triangleBEG BG=a/2, EG=(a/2)*sqrt(3)
: BE=a, so triangleABE is equilateral.
Regards, Peter Scales.

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