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Problem
Problem
In triangle
A
B
C
ABC
A
B
C
,
B
C
=
8
BC = 8
B
C
=
8
,
C
A
=
6
CA = 6
C
A
=
6
, and
A
B
=
10
AB = 10
A
B
=
10
. A line dividing the triangle
A
B
C
ABC
A
B
C
into two regions of equal area is perpendicular to
A
B
AB
A
B
at point
X
X
X
. Find the value of
B
X
2
\frac{BX}{\sqrt{2}}
2
B
X
.
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