MathDB

There is a circle

k

in a plane with center

M

and radius

r

. The following illustration, through which every point

P \ne M

., is called a “reflection on the circle

k

” from

\varepsilon

a point

P'

from

\varepsilon

is assigned:
(1)

P'

lies on the ray emanating from

M

and passing through

P

. (2) It is

MP \cdot MP' = r^2

.
a) Construct the mirror point

P'

for any given point

P \ne M

inside

k

.
b) Let another circle

k_1

be given arbitrarily, but such that

M

lies outside

k_1

.Construct

k'_1

, i.e. the set of all mirror points

P'

of the points

P

k_1

Problem Statement