FERMAT 2019 Problem 22

In the diagram, two circles touch at P. Also, Q P and S U are perpendicular diameters of the larger circle that intersect at O. Point V is on Q P and V P is a diameter of the smaller circle. The smaller circle intersects S U at T, as shown. If Q V=9 and S T=5, what is the sum of the lengths of the diameters of the two circles?
fermat 2019 22

Answer Choices
A. 50
B. 91
C. 41
D. 82
E. 100