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KoMaL A Problems
KoMaL A Problems 2023/2024
A. 877
A. 877
Part of
KoMaL A Problems 2023/2024
Problems
(1)
Nice Nikolai Geometry
Source: Komal A. 877
4/12/2024
A convex quadrilateral
A
B
C
D
ABCD
A
BC
D
is circumscribed about circle
ω
\omega
ω
. A tangent to
ω
\omega
ω
parallel to
A
C
AC
A
C
intersects
B
D
BD
B
D
at a point
P
P
P
outside of
ω
\omega
ω
. The second tangent from
P
P
P
to
ω
\omega
ω
touches
ω
\omega
ω
at a point
T
T
T
. Prove that
ω
\omega
ω
and circumcircle of
A
T
C
ATC
A
TC
are tangent.Proposed by Nikolai Beluhov, Bulgaria
geometry
circumcircle