Answer is b) 85/6

2*pi*r = 10*pi => r = 5

Then, PQ = 2r = 10
QZ = r = 5
XQ = XZ - QZ = 17 - 5 =12

Since

Now, consider triangles XYZ and XPQ

The line YZ is perpendicular to the radius at the point of intersection.

Hence, PQ is parallel to YZ

This means that angle P = angle Y and angle Q = angle Z

We also have angle X is common,

This means that XYZ AND ZPQ are similar

=> YZ/XZ = PQ/XQ

=> YZ/17 = 10/12

=> YZ = 5/6 * 17

=> YZ = 85/6

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