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**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 **

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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.

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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.

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**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.**

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**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. **

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