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Let the base A B of a triangle A B C be ...

Let the base `A B` of a triangle `A B C` be fixed and the vertex `C` lies on a fixed circle of radius `rdot` Lines through `Aa n dB` are drawn to intersect `C Ba n dC A ,` respectively, at `Ea n dF` such that `C E: E B=1:2a n dC F : F A=1:2` . If the point of intersection `P` of these lines lies on the median through `A B` for all positions of `A B ,` then the locus of `P` is
(a) a circle of radius `r/2` (b) a circle of radius `2r` (c) a parabola of latus rectum `4r` (d) a rectangular hyperbola

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