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Two variable chords \( A B \) and \( B C \) of a circle \( x^{2}+y^{2}=a^{2} \) are such
P that \( A B=B C=a \). \( M \) and \( N \) are the midpoints of \( A B \) and \( B C \),

W respectively, such that the line joining \( M N \) intersects the circles at \( P \) and \( Q \), where \( P \) is closer to \( A B \) and \( O \) is the center of the circle.
The locus of the point of intersection of tangents at \( A \) and \( C \) is
(1) \( x^{2}+y^{2}=a^{2} \)
(2) \( x^{2}+y^{2}=2 a^{2} \)
(3) \( x^{2}+y^{2}=4 a^{2} \)
(4) \( x^{2}+y^{2}=8 a^{2} \)
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