Geometry:

Circles Tangent to Each Other

Just like lines can be tangent to circles, circles can also be tangent to each other. There are two types of tangent circles. If one circle is inside the other, then they are internally tangent. If not, then they are externally tangent.

• INTERNALLY TANGENT:

  

  Point A is the center of the big circle. Point B is the center of the small circle. Point P is the point of tangency. Notice a few useful facts:

  P is the only point that lies on both circles A and B.

  Points A, B, and P are collinear (they all lie on the same straight line).

  The distance AB (the distance between the circles' centers) is the difference between radii AP and BP.

• EXTERNALLY TANGENT:

  

  Points A and B are the centers of the circles. Point P is the point of tangency. Notice a few useful facts:

  Again, P is the only point that lies on both circles A and B.

  Again, points A, B, and P are collinear.

  The distance AB (the distance between the circles' centers) is the sum of radii AP and BP.