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?
Experimenting with the size of BC, as it gets closer to being a diameter, at some point both nappes of the hyperbola lie outside the circle (on the same side of the circle, so that the circle lies within one of the nappes of the hyperbola). Another question is at what size segment BC causes this to happen.
re: GSP exploration
