Let ABC be a triangle with BC=13,CA=11,AB=10. Let A1 be the midpoint of BC. A variable line ℓ passes through A1 and meets AC,AB at B1,C1. Let B2,C2 be points with B2B=B2C,B2C1⊥AB,C2B=C2C,C2B1⊥AC, and define P=BB2∩CC2. Suppose the circles of diameters BB2,CC2 meet at a point Q=A1. Given that Q lies on the same side of line BC as A, the minimum possible value of PCPB+QCQB can be expressed in the form cab for positive integers a,b,c with gcd(a,c)=1 and b squarefree. Determine a+b+c.Proposed by Vincent Huang