Kristen Robinson

EMAT 4680

3 October 2000

Assignment 13 Number 4

The task was , given three points A, B, and C, draw a line intersecting AC in the point X and BC in the point Y such that AX = XY = YB. To complete this construction, construct a point on AC, X. Next construct a circle by center and radius with center X and radius AX. Also construct a circle by center and radius with center B and radius AX. Where these two circles intersect on segment BC is the location of point Y. To find this point of intersection, construct the point of intersection of the circle centered at X and the segment BC, E. Also construct the point of intersection of the circle centered at B and the segment BC, Y. Measure the distance between these two points. When the distance equals zero, E = Y. So XE = BY. So XY = BY. Because the circles were constructed with a radius equal to AX, AX = XY = BY.