Circle Tangency
Lesson · Beginner
Geometry: Plane Geometry
1. Tangent and Radius
The radius is perpendicular to the tangent line.
2. Two Tangents from an External Point
If two tangents are drawn from the same external point, their lengths are equal.
3. Two Tangent Circles
When two circles are tangent, the centers and the tangent point are collinear.
For externally tangent circles:
4. One Circle Inside Another (Internally Tangent)
For internally tangent circles:
Two circles of radii and are externally tangent. Find the length of their common tangent in terms of and .
Two circles of radii 9 and 16 are externally tangent. A third circle is externally tangent to both of them and also tangent to their common external tangent line.
Find the radius of the third circle if it lies between the first two circles.
For two circles with radii and that are externally tangent, the length of their common tangent is
So
For two circles with radii and whose centers are distance apart, the length of an external common tangent segment is
As a special case, when the two circles are externally tangent,
Draw the perpendicular from to the line , meeting it at .
By the Pythagorean theorem in the right triangle ,
As a special case, when the two circles are externally tangent,
For two circles with radii and whose centers are distance apart, the length of an internal common tangent segment is
