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2014 Irish Math Olympiad
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Part of
2014 Irish Math Olympiad
Problems
(1)
Geometry Irish MO
Source: Irish Mathematical Olympiad 2014 Paper 2 Question 2
4/20/2017
The square
A
B
C
D
ABCD
A
BC
D
is inscribed in a circle with center
O
O
O
. Let
E
E
E
be the midpoint of
A
D
AD
A
D
. The line
C
E
CE
CE
meets the circle again at
F
F
F
. The lines
F
B
FB
FB
and
A
D
AD
A
D
meet at
H
H
H
. Prove
H
D
=
2
A
H
HD = 2AH
HD
=
2
A
H
geometry