A circle \( C_{1} \) passes through the origin \( O \) and has diameter 4 on the positive \( x \...

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A circle \( C_{1} \) passes through the origin \( O \) and has diameter 4 on the positive \( x \)-axis. The line \( y=2 x \) gives a chord \( O A \) of circle \( C_{1} \). Let \( C_{2} \) be the circle with \( O A \) as a diameter. If the tangent to \( C_{2} \) at the point \( A \) meets the \( x \)-axis at \( P \) and \( y \)-axis at \( Q \), then \( Q A: A P \) is equal to :
(a) \( 1: 4 \)
(b) \( 1: 5 \)
(c) \( 2: 5 \)
(d) \( 1: 3 \)
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