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Circle Tangency

Lesson · Beginner

Geometry: Plane Geometry

1. Tangent and Radius

A tangent line perpendicular to the radius at the point of tangency

The radius is perpendicular to the tangent line.

OP⊥tangent OP\perp\text{tangent}

2. Two Tangents from an External Point

Two tangents drawn from the same external point

If two tangents are drawn from the same external point, their lengths are equal.

AB=AC AB=AC

3. Two Tangent Circles

When two circles are tangent, the centers and the tangent point are collinear.

Two externally tangent circles with centers and tangent point collinear

For externally tangent circles:

O1, P, O2 are collinear O_1,\ P,\ O_2\text{ are collinear}
O1O2=R1+R2 O_1O_2=R_1+R_2

4. One Circle Inside Another (Internally Tangent)

One circle internally tangent to another with centers and tangent point collinear

For internally tangent circles:

O1, O2, P are collinear O_1,\ O_2,\ P\text{ are collinear}
O1O2=R2−R1 O_1O_2=R_2-R_1
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