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Mathematics
Mathematics
Problem
In
△
X
Y
Z
\triangle XYZ
△
X
Y
Z
, point
P
P
P
lies on side
X
Y
XY
X
Y
such that
X
P
=
P
Y
XP = PY
X
P
=
P
Y
. A line through
P
P
P
parallel to
Y
Z
YZ
Y
Z
meets
X
Z
XZ
X
Z
at point
Q
Q
Q
. a. (a) Prove that
P
P
P
is the midpoint of
X
Y
XY
X
Y
. b. (b) Prove that
Q
Q
Q
is the midpoint of
X
Z
XZ
X
Z
. c. (c) If
Y
Z
=
10
cm
YZ = 10\,\text{cm}
Y
Z
=
10
cm
, find the length of
P
Q
PQ
P
Q
.
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