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
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.