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

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Peter Scales

Posts: 192
From: Australia
Registered: 4/3/05
Re: Three points on incircle
Posted: Apr 30, 2014 2:10 PM
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> 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.

Hi Avni,

Construct the unit circle and points A and B
Construct P(2/5,1/5) with OP=1/sqrt(5)
Circle centre O, radius OP meets ox in Q(1/sqrt(5),0)
Vertical thru Q meets unit circle at D and E,
with y = +- 2/sqrt(5)
Line AD meets unit circle at F(-sqrt(5)/3,-2/3)
B,E,F are collinear.

Regards, Peter Scales.

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