Tangents and Circles

1. Tangents and Circles

2. Tangent Definition • A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.

3. Theorem 1 The radius of a circle is perpendicular to a tangent of that circle

4. Theorem 2 Tangent segments to a circle from the same external point are congruent

5. 2 completely separate circles = 4 Common Tangents • 2 external tangents (blue) • 2 internal tangents (black)

6. 2 externally tangent circles = 3 Common Tangents • 2 external tangents (blue) • 1 internal tangent (black)

7. 2 overlapping circles 2 Common Tangents • 2 external tangents (blue) • 0 internal tangents

8. 2 internally tangent circles One Common Tangent • 1 external tangent (blue) • 0 internal tangents

9. 0 Common Tangents (2 concentric circles)Concentric circles are circleswith the same center. • 0 external tangents • 0 internal tangents • (one circle floating inside the other, without touching) • 0 external tangents • 0 internal tangents