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

hard

Point upper V lies on side upper X upper Y.
- The length of line segment X upper V is c.
- The length of line segment upper V upper Y is a.
Point upper W lies on side upper Y upper Z.
- The length of line segment upper Y upper W is b.
- The length of line segment upper W upper Z is d.
The length of side upper X upper Z is 99.
The length of line segment upper V upper W is 54.
Note: Figure not drawn to scale.

In triangle XYZ, $\frac{a}{c}=k$ and $\frac{b}{d}=k$. What is the value of $k$?

A

$\frac{6}{11}$

B

$\frac{6}{5}$

C

$\frac{11}{6}$

D

$\frac{11}{5}$