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2001 Spain Mathematical Olympiad
Problem 5
Problem 5
Part of
2001 Spain Mathematical Olympiad
Problems
(1)
2001 Spain Mathematical Olympiad, Problem 5
Source: Spain Mathematical Olympiad 2001
6/6/2017
A quadrilateral
A
B
C
D
ABCD
A
BC
D
is inscribed in a circle of radius 1 whose diameter is
A
B
AB
A
B
. If the quadrilateral
A
B
C
D
ABCD
A
BC
D
has an incircle, prove that
C
D
≤
2
5
−
2
CD \leq 2 \sqrt{5} - 2
C
D
≤
2
5
−
2
.
geometry