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?