I will discuss three unrelated sets of results combining geometry and algorithms. First we will see classes of graphs defined using the intersection of geometric objects in the plane, and discuss classical optimization problems for them. Then we will consider approximation algorithms for the potato peeling problem: find a maximum-area convex body inside a given polygon. The problem amounts to finding a maximum clique in the visibility graph of random samples of points inside the polygon, and results from stochastic geometry are used to bound the size of the samples. Finally, we will discuss the efficient computation of Shapley values for coalitional games defined by the area of usual geometric objects, such as the convex hull or the minimum axis-parallel bounding box.