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

hard

In the figure, $\overline{LQ}$ intersects $\overline{MP}$ at point $R$, and $\overline{LM}$ is parallel to $\overline{PQ}$. The lengths of $\overline{MR},\overline{LR}$, and $\overline{RP}$ are $9,10$, and $19$, respectively. [cite: 1830, 1831]

What is the length of $\overline{LQ}$?

A

280/19

B

190/9

C

271/9

D

280/9