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Kvant Problems
Kvant 2023
M2743
M2743
Part of
Kvant 2023
Problems
(1)
Geometry with circles and triangle
Source: 44th International Tournament of Towns, Senior A-Level P2, Spring 2023
4/4/2023
Perimeter of triangle
A
B
C
ABC
A
BC
is
1
1
1
. Circle
ω
\omega
ω
touches side
B
C
BC
BC
, continuation of side
A
B
AB
A
B
at
P
P
P
and continuation of side
A
C
AC
A
C
in
Q
Q
Q
. Line through midpoints
A
B
AB
A
B
and
A
C
AC
A
C
intersects circumcircle of
A
P
Q
APQ
A
PQ
at
X
X
X
and
Y
Y
Y
. Find length of
X
Y
XY
X
Y
.
geometry