# Tangent Cuts

Geometry Level 4

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 $$RS$$?

×