2013 AIME II Problem 10

Given a circle of radius \sqrt{13}, let A be a point at a distance 4 + \sqrt{13} from the center O of the circle. Let B be the point on the circle nearest to point A. A line passing through the point A intersects the circle at points K and L. The maximum possible area for \triangle BKL can be written in the form \frac{a - b\sqrt{c}}{d}, where a, b, c, and d are positive integers, a and d are relatively prime, and c is not divisible by the square of any prime. Find a+b+c+d.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.