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National and Regional Contests
India Contests
NMTC
2023 NMTC Junior
P8
P8
Part of
2023 NMTC Junior
Problems
(1)
NMTC Junior 2023 P8
Source: NMTC Junior 2023 P8
11/8/2023
A
B
C
D
ABCD
A
BC
D
is a cyclic quadrilateral. The midpoints of the diagonals
A
C
AC
A
C
and
B
D
BD
B
D
are respectively
P
P
P
and
Q
Q
Q
. If
B
D
BD
B
D
bisects
∠
A
Q
C
\angle AQC
∠
A
QC
, the prove that
A
C
AC
A
C
will bisect
∠
B
P
D
\angle BPD
∠
BP
D
.
geometry
nmtc
cyclic quadrilateral