Amberly Roberts
Assignment 7: Tangent Circles
We will investigate the following:
Given two circles and a point on one of the circles, construct a circle tangent to the two circles with one point of tangency being the designated point.
Before we start, we must consider the various ways in which the two initial circles can be placed. There are two solutions for each case. Thus, the investigation will take you through 6 different constructions.
Case 1 One circle is inside the other 
Case 2 the circles intersect at two different points 
Case 3 the circles are placed in the same plane, have no points of intersection, and share no common interior points 

It's definitely easier to complete this investigation by constructing a sketch of the final drawing and working backwards. It's a little easier to formulate conjectures using this method.
The locus of the center of circle C (the tangent circle) is shown in pink in the construction to the right. As point F (the designated point) moves, the tangent circle will certainly change. The locus shows all possible places for the center of that solution circle to be. In this case, the locus is an ellipse. 

CASE 1: First Solution 
The locus of the center of circle C (the tangent circle) is shown in pink in the construction to the right. As point F (the designated point) moves, the tangent circle will certainly change. The locus shows all possible places for the center of that solution circle to be. In this case, the locus is an ellipse.


CASE 1: Second Solution 
The locus of the center of circle C (the tangent circle) is shown in pink in the construction to the right. As point F (the designated point) moves, the tangent circle will certainly change. The locus shows all possible places for the center of that solution circle to be. In this case, the locus is an ellipse.


CASE 2: First Solution 
The locus of the center of circle C (the tangent circle) is shown in pink in the construction to the right. As point F (the designated point) moves, the tangent circle will certainly change. The locus shows all possible places for the center of that solution circle to be. In this case, the locus is a hyperbola.


CASE 2: Second Solution 
The locus of the center of circle C (the tangent circle) is shown in pink in the construction to the right. As point F (the designated point) moves, the tangent circle will certainly change. The locus shows all possible places for the center of that solution circle to be. In this case, the locus is a hyperbola.


CASE 3: First Solution 
The locus of the center of circle C (the tangent circle) is shown in pink in the construction to the right. As point F (the designated point) moves, the tangent circle will certainly change. The locus shows all possible places for the center of that solution circle to be. In this case, the locus is a hyperbola.


CASE 3: Second Solution 
Click here to open GSP which contains a script tool for constructing a tangent circle.
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