Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


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

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Peter Scales

Posts: 153
From: Australia
Registered: 4/3/05
Re: Three points on incircle
Posted: Apr 28, 2014 1:04 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> Let ABC be an equilateral triangle with side length a
> = 2. Construct points D, E, F on the incircle, such
> that triples {C,D,E}, {B,E,F}, {A,F,D} are collinear
> respectively.
>
>
> Best regards,
> Avni

Hi Avni,

Let incenter = I
Bisect BI at H and construct circle on BI as diameter
Bisect HI at J and construct circle, center I, radius IJ
to intersect first circle at G.
Then G is the mid-point of EF and B,E,F are collinear
sin(angleIBG)=((inradius/2)/circumradius)=1/4
So angle between side BA and side EF =Pi/6-arcsin(1/4)
=30-14.48degrees=15.52deg approx.

Regards, Peter Scales.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.