20th CanMO 1988 Problem 2 Given a triangle area A and perimeter p, let S be the set of all points a distance 5 or less from a point of the triangle. Find the area of S.
S is the triangle itself (and all its interior points), a rectangle width 5 on each side and the sector of a circle radius 5 at each vertex to join together the two rectangles. The three sectors together form a circle. Hence the area of S is A + 5p + 25 π. 20th CanMO 1988 © John Scholes jscholes@kalva.demon.co.uk 21 June 2002