Computing geometric properties of a union of spheres is important to many 3 applications in computational biology. The following problem is a 2-dimensional simplification of one of these problems. You are given a set P of atoms forming a protein, which for our purposes will be represented by a collection of circles in the plane, all of equal radius r_a. Such a protein lives in a solution of water. We will model a molecule of water by a circle of radius r_b > r_a. We say that an atom a ? P is solvent-accessible if there exists a placement of a water molecule that is tangent to a, and the water molecule does not intersect any other atoms in P. In the figure below, all atoms are solvent-accessible except for three (shaded). Given a protein molecule P of n atoms, devise an O(n log n) time algorithm to determine all solventinaccessible atoms of P.

Please write the algorithm, a justification of its correctness, and a derivation of its running time. Write clear and convincing PSEUDO-CODE for your algorithm. NO CODE.