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Bulgarian Spring Mathematical Competition
2023 Bulgarian Spring Mathematical Competition
9.2
9.2
Part of
2023 Bulgarian Spring Mathematical Competition
Problems
(1)
Weird cyclic quadrilateral to prove
Source: Bulgarian Spring Tournament 2023 9.2
3/25/2023
Given is triangle
A
B
C
ABC
A
BC
with angle bisector
C
L
CL
C
L
and the
C
−
C-
C
−
median meets the circumcircle
Γ
\Gamma
Γ
at
D
D
D
. If
K
K
K
is the midpoint of arc
A
C
B
ACB
A
CB
and
P
P
P
is the symmetric point of
L
L
L
with respect to the tangent at
K
K
K
to
Γ
\Gamma
Γ
, then prove that
D
L
C
P
DLCP
D
L
CP
is cyclic.
geometry