Explortations with Geometer's Sketchpad

Given three points A, B, and C. Find a point on CA, call it X, and a point on CB call it y so that AX= XY = YB.

Let's draw AB with a dotted line and pick a point on CA, called x'.

Now we want to construct a rhombus with two sides parallell to CB. So, construct a line parallel CB through x'. Also construct a circle with center at x' with radius X'A.

Next we need to find a point on AB, w' so that the length of Y'W' is the same as X'Y'. To find this point construct a circle with center y' and radius X'Y',


To get the rhombus we need constrcut the segment y'w', construct a line parallell to y'w' through x', and make off v'x'.

By constructing the line Av' we can locate the point Y on CB and using YB as a radius and A as the center of a circle we can locate X.

To finish lets clean up our drawing and check to be sure AX = XY = YB