2. The Spiral of Archimedes The spiral of Archimedes can be used to trisect an angle. Given a spiral, place the angle to be trisected so that the vertex and the initial side of the angle coincide with the initial point of the spiral and the initial position OA of the rotating ray. Let the terminal side of the angle intersect the spiral of P. Trisect the segment OP at the points Q and R, and draw circles with center at O and with OQ and OR as radii. Prove that if these circles meet the spiral in points U and V, then the lines OU and OV will trisect angle AOP. R Spiral A

Fig: 1