3rd CaMO 1971 Problem 1 A diameter and a chord of a circle intersect at a point inside the circle. The two parts of the chord are length 3 and 5 and one part of the diameter is length 1. What is the radius the circle?
Let the chord be AB, the diameter be CD and the point of intersection X. Then XA.XB = XC.XD, so the other part of the diameter has length 15. So the diameter has length 16 and the radius is 8. 3rd CaMO 1971 © John Scholes jscholes@kalva.demon.co.uk 10 June 2002