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Mathematics
Problem
In a tetrahedron
O
A
B
C
OABC
O
A
B
C
, the edges are of lengths,
∣
O
A
∣
=
∣
B
C
∣
=
a
|OA| = |BC| = a
∣
O
A
∣
=
∣
B
C
∣
=
a
,
∣
O
B
∣
=
∣
A
C
∣
=
b
|OB| = |AC| = b
∣
O
B
∣
=
∣
A
C
∣
=
b
,
∣
O
C
∣
=
∣
A
B
∣
=
c
|OC| = |AB| = c
∣
O
C
∣
=
∣
A
B
∣
=
c
. Let
G
1
G_1
G
1
and
G
2
G_2
G
2
be the centroids of the triangle
A
B
C
ABC
A
B
C
and
A
O
C
AOC
A
O
C
such that
O
G
1
⊥
B
G
2
OG_1 \perp BG_2
O
G
1
⊥
B
G
2
, then the value of
a
2
+
c
2
b
2
\frac{a^2 + c^2}{b^2}
b
2
a
2
+
c
2
is a. 2 b. 3 c. 6 d. 9
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