MathDB

Let

C

be a circle with center

M

in a plane

V

, and

P

be a point not on the circle

C

(a)

P

is fixed, prove that AP^2\plus{}BP^2 is a constant for every diameter

AB

of the circle

C

(b)

Let

AB

be a fixed diameter of

C

and

P

a point on a fixed sphere

S

not intersecting

V

. Determine the points

P

S

that minimize AP^2\plus{}BP^2.

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