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New Zealand Contests
Auckland Mathematical Olympiad
2023 Auckland Mathematical Olympiad
9
9
Part of
2023 Auckland Mathematical Olympiad
Problems
(1)
d(O,AC)= 1/2 BC, cyclic ABCD, AC_|_BD (2023 Auckland MO p9)
Source:
3/26/2024
Quadrillateral
A
B
C
D
ABCD
A
BC
D
is inscribed in a circle with centre
O
O
O
. Diagonals
A
C
AC
A
C
and
B
D
BD
B
D
are perpendicular. Prove that the distance from the centre
O
O
O
to
A
D
AD
A
D
is half the length of
B
C
BC
BC
.
geometry