MathDB

Given a plane

P

and two fixed points

A

and

B

that do not lie in this plane. Denote two points

A'

and

B'

on plane

P

and

M ,N

the midpoints of the segments

AA'

BB'

. a) Determine the locus of the midpoint of the segment MN if the points are

A'

and

B'

move arbitrarily in plane

P

. b) A circle

O

is considered in the plane

P

. Determine the locus

L

of the midpoint of the segment

MN

if the points

A'

and

B'

lie on the circle

O

or inside it . c)

A'

is assumed to be fixed on the circle

O

or inside it and

B'

is assumed to be movable inside it , except for

O

. Determine the locus of the point

B'

such the above certain locus

L

remains the same . Note: For b) and c) the following cases should be considered: 1.

A'

and

B'

are different, 2.

A'

and

B'

coincide.

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