Circles ω and γ, both centered at O, have radii 20 and 17, respectively. Equilateral triangle ABC, whose interior lies in the interior of ω but in the exterior of γ, has vertex A on ω, and the line containing side BC is tangent to γ. Segments AO and BC intersect at P, and CPBP=3. Then AB can be written in the form nm−qp for positive integers m, n, p, q with gcd(m,n)=gcd(p,q)=1. What is m+n+p+q?
<spanclass=′latex−bold′>(A)</span>42<spanclass=′latex−bold′>(B)</span>86<spanclass=′latex−bold′>(C)</span>92<spanclass=′latex−bold′>(D)</span>114<spanclass=′latex−bold′>(E)</span>130