Problem (Geometry):
Let $T=1$. Circles $L$ and $O$ are internally tangent and have radii $T$ and $4 T$, respectively. Point $E$ lies on circle $L$ such that $\overline{O E}$ is tangent to circle $L$. Compute $O E$.

Solution:
Because $\overline{O E}$ is tangent to circle $L, \overline{L E} \perp \overline{O E}$. Also note that $L O=4 T-T=3 T$. Hence, by the Pythagorean Theorem, $O E=\sqrt{(3 T)^{2}-T^{2}}=2 T \sqrt{2}$ (this also follows from the TangentSecant Theorem). With $T=1, O E=\mathbf{2} \sqrt{\mathbf{2}}$.

Final answer: $2 \sqrt{2}$