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National and Regional Contests
Bulgaria Contests
Bulgaria National Olympiad
1986 Bulgaria National Olympiad
Problem 5
Problem 5
Part of
1986 Bulgaria National Olympiad
Problems
(1)
locus as point defines circle
Source: Bulgaria 1986 P5
6/15/2021
Let
A
A
A
be a fixed point on a circle
k
k
k
. Let
B
B
B
be any point on
k
k
k
and
M
M
M
be a point such that
A
M
:
A
B
=
m
AM:AB=m
A
M
:
A
B
=
m
and
∠
B
A
M
=
α
\angle BAM=\alpha
∠
B
A
M
=
α
, where
m
m
m
and
α
\alpha
α
are given. Find the locus of point
M
M
M
when
B
B
B
describes the circle
k
k
k
.
Locus
geometry
circles