3.1 Let BC be a fixed line segment of length d in the plane. Let A be a point which moves such that sum of the lengths AB and AC is a constant k. Find the maximum value of the area of the triangle AABC. = = 3.2 Let A == (0, 1) and B (2,0) in the plane. Let O be the origin and C (2,1). Let P move on the segment OB and let Q move on the segment AC. Find the coordinates of P and Q for which the length of the path con- sisting of the segments AP, PQ and QB is least. 3.3 A regular 2N-sided polygon of perimeter L has its vertices lying on a circle. Find the radius of the circle and the area of the polygon. 3.4 Let BC be a fixed line segment of length d and let S be a fixed point whose distance from the line BC is 2a. A point A moves such that the alti- tude of the triangle AABC from the vertex A is equal to the length of the line segment AS. Find the minimum possible value of the area of the triangle . 3.5 Pick out the bounded sets: a. S is the set of all points in the plane such that the product of its distances from a fixed pair of orthogonal straight lines is a constant; b. S={(x, y) 4x2 -2xy + y = 1}; c. S = {(x, y) ; x + y = 1}.