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Russia Contests
All-Russian Olympiad
1962 All-Soviet Union Olympiad
2
2
Part of
1962 All-Soviet Union Olympiad
Problems
(1)
Locus of a tangent point
Source: 1962 All-Soviet Union Olympiad
1/15/2018
Given a fixed circle
C
C
C
and a line L through the center
O
O
O
of
C
C
C
. Take a variable point
P
P
P
on
L
L
L
and let
K
K
K
be the circle with center
P
P
P
through
O
O
O
. Let
T
T
T
be the point where a common tangent to
C
C
C
and
K
K
K
meets
K
K
K
. What is the locus of
T
T
T
?
geometry
Locus
Russia