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10
2004 HMMT Geometry # 10
2004 HMMT Geometry # 10
Source:
March 3, 2024
geometry
Problem Statement
Right triangle
X
Y
Z
XY Z
X
Y
Z
has right angle at
Y
Y
Y
and
X
Y
=
228
XY = 228
X
Y
=
228
,
Y
Z
=
2004
Y Z = 2004
Y
Z
=
2004
. Angle
Y
Y
Y
is trisected, and the angle trisectors intersect
X
Z
XZ
XZ
at
P
P
P
and
Q
Q
Q
so that
X
X
X
,
P
P
P
,
Q
Q
Q
,
Z
Z
Z
lie on
X
Z
XZ
XZ
in that order. Find the value of
(
P
Y
+
Y
Z
)
(
Q
Y
+
X
Y
)
(PY + Y Z)(QY + XY )
(
P
Y
+
Y
Z
)
(
Q
Y
+
X
Y
)
.
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