MathDB

Two straight lines

p, q

are given in the plane and on the straight line

q

there is a point

F

F \not\in p

. Determine the set of all points

X

that can be obtained by this construction: In the plane we choose a point

S

that lies neither on

p

nor on

q

, and we construct a circle

k

with center

S

that is tangent to the line

p

. On the circle

k

we choose a point

T

such that so that

ST \parallel q

. If the line

FT

intersects the line

p

at the point

U

X

is the intersection of the lines

SU

and

q

Problem Statement