Points $A$ and $B$ lie on circle $\omega$.  Point $P$ lies on the extension of segment $AB$ past $B$.  Line $\ell$ passes through $P$ and is tangent to $\omega$.  The tangents to $\omega$ at points $A$ and $B$ intersect $\ell$ at points $D$ and $C$ respectively.  Given that $AB=7$, $BC=2$, and $AD=3$, compute $BP$.

Let's think step by step and output the final answer within \boxed{}.
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