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11
Math Prize 2022 Problem 11
Math Prize 2022 Problem 11
Source:
October 12, 2022
Problem Statement
Let
A
A
A
,
B
B
B
,
C
C
C
,
D
D
D
,
E
E
E
, and
F
F
F
be
6
6
6
points around a circle, listed in clockwise order. We have
A
B
=
3
2
AB = 3\sqrt{2}
A
B
=
3
2
,
B
C
=
3
3
BC = 3\sqrt{3}
BC
=
3
3
,
C
D
=
6
6
CD = 6\sqrt{6}
C
D
=
6
6
,
D
E
=
4
2
DE = 4\sqrt{2}
D
E
=
4
2
, and
E
F
=
5
2
EF = 5\sqrt{2}
EF
=
5
2
. Given that
A
D
‾
\overline{AD}
A
D
,
B
E
‾
\overline{BE}
BE
, and
C
F
‾
\overline{CF}
CF
are concurrent, determine the square of
A
F
AF
A
F
.
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