MathDB

Let

d

be a diameter of a circle

k

, and let

A

be an arbitrary point on this diameter

d

in the interior of

k

. Further, let

P

be a point in the exterior of

k

. The circle with diameter

PA

meets the circle

k

at the points

M

and

N

.
Find all points

B

on the diameter

d

in the interior of

k

such that \measuredangle MPA = \measuredangle BPN \text{and} PA \leq PB. (i. e. give an explicit description of these points without using the points

M

and

N

Problem Statement