Case 1: One circle is INSIDE the other. In this case, there are actually two different circles that will be tangent to our original circle.
Case 2: The circles intersect. In this case, there are still two tangent circles.
Case 3: The two circles are disjoint. The result is two tangent circles with one so large it approaches being a line.
Click here to open a GSP sketch with a tool to construct the circles tangent to two given circles.
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Click here to open a GSP sketch with a tool to construct the circles tangent to the circle and line.
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