Triangle △ABC has sidelengths AB=10, AC=14, and, BC=16. Circle ω1 is tangent to rays AB, AC and passes through B. Circle ω2 is tangent to rays AB, AC and passes through C. Let ω1, ω2 intersect at points X,Y . The square of the perimeter of triangle △AXY is equal to da+bc , where a,b,c, and, d are positive integers such that a and d are relatively prime, and c is not divisible by the square of any prime. Find a+b+c+d.