Problem # 3

The purpose of this assignment is to construct a circle tangent to the two circles with one point of tangency being the designated point when given two circles and a point on one of the circles. The described situation is illustrated below.

At this point, we shall also construct an isosceles triangle with vertices at the center of the large circle, the center of one of the small circles, and one endpoint of the diameter of the second small circle. Our picture would then resemble the following.

Next, we want to trace the the center of the large circle and examine the locus of points created by the trace.

It appears as though the shape that the point traces out is an ellipse. In order to see a complete animation,

click here.

It is also possible to animate the base of the isosceles triangle and make note of whether or not the animation provides us with the same figure.

Just as we saw before, the figure is an ellipse.

click here for a full animation.

At this point we also wish to discuss the construction of tangent circles if the two given circles intersect. The picure below depicts the situation.

Next, we must trace the center of the larger, tangent circle.

Furthermore, we may also animate the segments from the centers of the given circles to the tangent circles and make any necessary observations.

Again, our end product appears to be an ellipse. If you wish to see the animation,

click here.

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