Description	Picture of Tangent Circle	Locus of Tangent Circle Center
Given: Two circles, one inside the other. The given point is on the large circle. The smaller of the given circle is exterior to the tangent circle.
Given: Two circles, one inside the other. The given point is on the large circle. The smaller of the given circle is interior to the tangent circle.
Given: Two circles, one inside the other. The given point is on the smaller circle. The smaller of the given circle is exterior to the tangent circle.
Given: Two circles, one inside the other. The given point is on the smaller circle. The smaller of the given circle is interior to the tangent circle.
Given: Two intersecting circles. The smaller circle is exterior to the tangent circle. The given point is on the larger circle.
Given: Two intersecting circles. The smaller circle is exterior to the tangent circle. The given point is on the smaller circle.

We see that all the loci of the tangent circle centers are ellipses. Sometimes this is not the case. Click here to explore the other option.

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