Assignment 6


Page Bird


6. 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





I first thought about this problem using circles.  Also, I wanted my GSP sketch to be dynamic.  So I started by constructing a random angle such as the one above.  From there, I randomly placed a point on segment AB.  This is point X.

Next, I used segment AX as the radius and point C as the center to create a congruent circle at point C.




The point where circle C intersects segment BC is point Y.  Now, using Y as the center and segment YC as the radius I constructed another circle.





Now, I was able to clear out the circles and connect X and Y to form segment XY.  From the clip below you can see the GSP measurements and can verify that AX=XY=YC.





To see a dynamic sketch of this picture click here.  You can control the size of the angle and segments several ways.  Dragging point A or Z are the best ways to control the angle size.