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Kvant 2024
M2794
M2794
Part of
Kvant 2024
Problems
(1)
Isogonal conjugate on (BIC)
Source: Kvant Magazine No. 5-6 2024 M2794
8/25/2024
The points
P
P
P
and
Q
Q
Q
lie inside the circle
ω
\omega
ω
. The perpendicular bisector to the segment
P
Q
PQ
PQ
intersects
ω
\omega
ω
at points
A
A
A
and
D
D
D
. A circle centered on
D
D
D
passing through
P
P
P
and
Q
Q
Q
intersects
ω
\omega
ω
at points
B
B
B
and
C
C
C
. The segment
P
Q
PQ
PQ
lies inside the triangle
A
B
C
ABC
A
BC
. Prove that
∠
A
C
P
=
∠
B
C
Q
\angle ACP = \angle BCQ
∠
A
CP
=
∠
BCQ
. Proposed by A. Zaslavsky
geometry