Circle \( \Gamma_1 \) centered at \(A\) has a smaller radius than circle \( \Gamma_2 \) centered at \(B\).

From \(A\), the tangents to \( \Gamma_2 \) intersect \( \Gamma_1 \) at \(P \) and \( Q \).

From \(B\), the tangents to \( \Gamma_1 \) intersect \( \Gamma_2 \) at \(R\) and \(S \).

Which line segment is longer, \( PQ \) or \( RS \)?

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