Our instructions are:

"Given two circles and a point on one of the cirlces. Construct a circle tangent to the two circles with one point of tangency being the designated point."

This may seem an impossible task, but a closer observation reveals that it is feasible and moreover, actually simple.

The video below illustrates a step by step process of constructing this tangent circle.

 

Can you finish the construction on your own?

Our newly constructed point at the intersection of the line that extends past the diameter of the blue circle and the line perpendicular to the green line, is the locus of the tangent circle we are constructing.

Construct a circle by clicking on this center and a point on the outside of the blue circle.

This is the tangent circle.

Click here to access the GSP file

Finally, to make your very own Tangent Circles, a script tool is given below.

Tangent Circles Script Tool

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