# Tangency Point of Two Circles: What is this about?

A Mathematical Droodle

What if applet does not run? |

(Points A and B move horizontally. Points C and D move vertically.)

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Copyright © 1996-2018 Alexander BogomolnyAssume two circles tangent to AB at A and B are also tangent to each other. What is the locus of their common point T when their radii change?

What if applet does not run? |

The locus is a circle with center at the midpoint of AB and the radius half its length. To see that draw the common tangent to the two circles at T to its intersection with AB at O. Then, since two tangents from a point to a circle are equal,

OA = OT = OB. |

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Copyright © 1996-2018 Alexander Bogomolny68054979