This construction allowed for the exploration of the relationship between different circles, where one is tangent to two different circles. In my exploration, I made the script tool as shown in the assignment. From this construction I was able to see that the locus of the centers of the tangent circles forms an ellipse with foci at the centers of the two circles. The trace of the ellipse can be seen by the tangent line that goes through the vertex of the isosceles triangle. This vertex lies on the perpendicular bisector and is the center of the tangent circle. When the circle is moved outside the original circle the ellipse becomes flatter and the tangent changes from the inside of one circle to the other where the circles intersect. At some point when moving the location of the circles, the trace of the locus of points appears to approach a circle. Below is the illustration of my exploration.
Click here to do an exploration using GSP.
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