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Math Forum » Discussions » Math Topics » geometry.puzzles.independent

Topic: Three points on incircle
Replies: 5   Last Post: May 29, 2014 3:04 PM

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Avni Pllana

Posts: 535
Registered: 12/6/04
Re: Three points on incircle
Posted: Apr 28, 2014 4:44 PM
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Hi Peter,

thanks for the contribution. The structure has an interesting property. Let BE = x, then the power of B with respect to the incircle is x*(1+x)= 1, or x = (sqrt(5)-1)/2, so we have the golden ratio.

The next problem is as follows:

Let A=[-1,-1], B=[1,-1]. Construct points D, E, F on the unit circle, such that line DE is parallel to the y-axis, and triples {B,E,F], {A,F,D} are collinear respectively.


Best regards,
Avni

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