What does it mean to say that two circles are "tangent"?

Click Here to see the definition of Tangent.

In today's lesson, here is the problem we are going to explore:

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.

Where do you think the center of the tangent circle might lie if the point of tangency is designated to be located on the larger circle?

How would you construct this tangent circle?

Click Here to see a GSP script.

What observations can you make about tangent circles in general?

Click Here to see several interesting observations made by the author.

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