Spatial queries can be expressed in terms of query regions of shapes other than the rectangle "windows" we have discussed in class. Popularly, a query can be expressed using a circle (e.g., a circular range search query can retrieve all hotels within 1km from one's current location) 1. Provide an analytical answer to the following question: Given a point p and a rectangle r in 2d space, what is the minimum distance between p and any point in r? [hint: consider regions of space with respect to the rectangle r] 2. We can employ an R-tree as index in order to evaluate a circular range search query. In order to do so, we need to solve the following problem: Given a rectangle r (the MBR of an R-tree node) and a circle c in 2d space (the query region), determine whether they intersect. Propose an efficient method that solves the above problem [hint: utilize your answer to question (1)] 3. The C-tree, by analogy to the R-tree, is another common spatial index used for evaluating spatial queries. Instead of using MBRs, as the R-tree does, the C-tree employs minimum bounding circles, i.e., circles of minimum area that enclose indexed objects and data points. The figure in the next page shows a C-tree indexing a set of points {a,b,c,d,e.f,g). Each minimum bounding circle is represented by its center and radius. For example, entry C? in the tree stores a triplet