Tangent circles

This is to explore tne construction of tangent circles. It begins with the following problem.Given two circles and a point one of the circles. Construct a circle tangent tp the two circles with one point of tangency being the designated point. Two cicles are tangent in two cases: interior case and exterior case.


INTERIOR CASE

Given two circles, the circle c1 with center A and the circle c2 with center B, we want to create a circle that is tangent both. The below figure is one of the possible figures. The circle c3 with ceter C is tangent to circles c1 and c2 so that smaller circle c2 is internal to the tangent circle c3. This case is called as the interior case.

Click here for the GSP file.

Click here for the GSP script.


EXTERIOR CASE

Given two circles, the circle c4 with center P and the circle c5 with center Q, we want to create a circle that is tangent both. The below figure is one of the possible figures. The circle c6 with center R is tangent to circles c3 and c4 so that smaller circle c5 is internal to the tangent circle c6. This case is called as the exterior case.

 

Click here for the GSP file.

Click here for the GSP script.


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