MathDB
Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
1998 Mexico National Olympiad
2
2
Part of
1998 Mexico National Olympiad
Problems
(1)
locus with circles
Source: Mexican Mathematical Olympiad 1998 OMM P2
7/28/2018
Rays
l
l
l
and
m
m
m
forming an angle of
a
a
a
are drawn from the same point. Let
P
P
P
be a fixed point on
l
l
l
. For each circle
C
C
C
tangent to
l
l
l
at
P
P
P
and intersecting
m
m
m
at
Q
Q
Q
and
R
R
R
, let
T
T
T
be the intersection point of the bisector of angle
Q
P
R
QPR
QPR
with
C
C
C
. Describe the locus of
T
T
T
and justify your answer.
geometry
Locus
circles