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8
2013 HMMT Geometry # 8
2013 HMMT Geometry # 8
Source:
March 3, 2024
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral. Extend line
C
D
CD
C
D
past
D
D
D
to meet line
A
B
AB
A
B
at
P
P
P
and extend line
C
B
CB
CB
past
B
B
B
to meet line
A
D
AD
A
D
at
Q
Q
Q
. Suppose that line
A
C
AC
A
C
bisects
∠
B
A
D
\angle BAD
∠
B
A
D
. If
A
D
=
7
4
AD = \frac{7}{4}
A
D
=
4
7
,
A
P
=
21
2
AP = \frac{21}{2}
A
P
=
2
21
, and
A
B
=
14
11
AB = \frac{14}{11}
A
B
=
11
14
, compute
A
Q
AQ
A
Q
.
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