Chords and arcs
YM is the chord of the circle and it has a length of 12 in
The perpendicular VL bisects the chord in V.
To prove the above statement, please note that triangles VYL and VLM are similar because they have one side in common and the second side of the same length (the radius of the circle).
Let's work with any of those triangles, for example, VLY. It's a right triangle in V. The hypotenuse of the triangle is the radius, one leg is the given distance of 5 in and the other leg is half the length of the chord (6 in).
Thus, applying Pythagora's Theorem:
Thus, the radius is
r=7.8 in
Option b.