MathDB

Let

AB

be a diameter of a circle,

C

be any fixed point between

A

and

B

on this diameter, and

Q

be a variable point on the circumference of the circle. Let

P

be the point on the line determined by

Q

and

C

for which \frac{AC}{CB}\equal{}\frac{QC}{CP}. Describe, with proof, the locus of the point

P

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