# Tangent Circles Make Great Triangles!

Geometry Level 3

Let $$\omega_1$$ and $$\omega_2$$ be two externally tangent circles at $$T$$ with $$\omega_1$$ smaller than $$\omega_2$$. Let their common external tangents intersect at $$S$$. Let a line through $$S$$ intersect circles $$\omega_1$$ and $$\omega_2$$ at $$A,B,C,D$$ in that order. Given that $$TC = 3$$ and $$TA = 4$$, find $$AC$$.

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