Circular permutations arise when objects are arranged around a circle or ring. Since rotations of the same arrangement are identical, fix one object and arrange the rest: (n-1)! ways. For necklaces and garlands where flips are also identical, divide by 2: (n-1)!/2. Geometry applications: number of triangles from n points (no three collinear) = C(n,3), quadrilaterals = C(n,4). If m points are collinear, subtract C(m,3) from total triangles. Number of diagonals of an n-gon = C(n,2) - n. Number of intersection points of n lines (no two parallel, no three concurrent) = C(n,2). These geometric counting problems appear regularly in JEE.