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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

In the figure, $\overline{LQ}$ and $\overline{MP}$ intersect at point $R$, and $\overline{LM}$ is parallel to $\overline{PQ}$. The lengths of $MR$, $LR$, and $RP$ are $6$, $7$, and $13$, respectively. What is the length of $LQ$?

1

133/6

2

22.17

3

22.16