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International Contests
Caucasus Mathematical Olympiad
2024 Caucasus Mathematical Olympiad
8
8
Part of
2024 Caucasus Mathematical Olympiad
Problems
(1)
Incircle geometry with locus
Source: Caucasus MO 2024, Seniors P8
3/13/2024
Let
A
B
C
ABC
A
BC
be an acute triangle and let
X
X
X
be a variable point on
A
C
AC
A
C
. The incircle of
△
A
B
X
\triangle ABX
△
A
BX
touches
A
X
,
B
X
AX, BX
A
X
,
BX
at
K
,
P
K, P
K
,
P
, respectively. The incircle of
△
B
C
X
\triangle BCX
△
BCX
touches
C
X
,
B
X
CX, BX
CX
,
BX
at
L
,
Q
L, Q
L
,
Q
, respectively. Find the locus of
K
P
∩
L
Q
KP \cap LQ
K
P
∩
L
Q
.
geometry