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2000 Portugal MO
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2000 Portugal MO
Problems
(1)
computational geometry, 2-digit lengths, rational 2000 Portugal p2
Source:
10/12/2020
In the figure, the chord
[
C
D
]
[CD]
[
C
D
]
is perpendicular to the diameter
[
A
B
]
[AB]
[
A
B
]
and intersects it at
H
H
H
. Length of
A
B
AB
A
B
is a two-digit natural number. Changing the order of these two digits gives length of
C
D
CD
C
D
. Knowing that distance from
H
H
H
to the center
O
O
O
is a positive rational number, calculate
A
B
AB
A
B
. https://cdn.artofproblemsolving.com/attachments/5/f/eb9c61579a38118b4f753bbc19a9a50e0732dc.png
geometry
circle