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Mathematics
Mathematics
Problem
Let
O
A
=
a
\mathbf{OA} = \mathbf{a}
OA
=
a
,
O
B
=
10
a
+
2
b
\mathbf{OB} = 10\mathbf{a} + 2\mathbf{b}
OB
=
10
a
+
2
b
and
O
C
=
b
\mathbf{OC} = \mathbf{b}
OC
=
b
, where
O
O
O
,
A
A
A
and
C
C
C
are non-collinear points. Let
p
p
p
denote the area of quadrilateral
O
A
C
B
OACB
O
A
C
B
, and let
q
q
q
denote the area of parallelogram with
O
A
\mathbf{OA}
OA
and
O
C
\mathbf{OC}
OC
as adjacent sides. If
p
=
k
q
p = kq
p
=
k
q
, find the numerical value of
k
k
k
.
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