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Mathematics
Mathematics
Problem
Let
O
O
O
be the origin and
O
P
OP
O
P
and
O
Q
OQ
O
Q
be the tangents to the circle
x
2
+
y
2
−
6
x
+
4
y
+
8
=
0
x^2 + y^2 - 6x + 4y + 8 = 0
x
2
+
y
2
−
6
x
+
4
y
+
8
=
0
at the points
P
P
P
and
Q
Q
Q
on it. If the circumcircle of the
Δ
O
P
Q
\Delta OPQ
Δ
O
P
Q
passes through the point
(
α
,
1
2
)
\left(\alpha, \frac{1}{2}\right)
(
α
,
2
1
)
, then a value of
α
\alpha
α
is (a)
5
2
\frac{5}{2}
2
5
(b) 1 (c)
−
1
2
-\frac{1}{2}
−
2
1
(d)
3
2
\frac{3}{2}
2
3
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