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LOP (Posted on 2017-12-13) Difficulty: 4 of 5

  
Let B and C be two fixed points on a circle with a center O
such that the points B, C, and O are not collinear. Let A be
a variable point on the same circle (distinct from points B
and C and the perpendicular bisector of BC). Let E and F
be the midpoints of BC and AO respectively. Let ray AE
intersect the circle again at point D. Let lines DO and EF
intersect at point P.

What is the locus of point P as point A moves around the
circle?
  

No Solution Yet Submitted by Bractals    
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re(2): GSP exploration | Comment 6 of 7 |
(In reply to re: GSP exploration by Bractals)

I found the hyperbola as well, using version 4.00.  Using coordinates I was able to find, for a specific choice of B and C, something that resembles the parametric equation.  Not ready to post yet.


One way to prove a hyperbola, find the foci F1 and F2 and show for every point P that |PF1-PF2|=constant.
One focus is the center of the circle.

  Posted by Jer on 2017-12-14 10:36:12
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