Circle Tangents and Intersection Points Guide

1. Section 10-1 Tangents to Circles

2. Center P Circle • The set of all points in a plane that are equidistant from a given point (center). Circles are named by their center! Circle P

3. Interior of a circle • Consists of the points inside the circle Exterior of a circle • Consists of the points outside the circle

4. L A N G E P

5. P Radius Radius • The distance from the center of a circle to a point on the circle

6. Radius • Segment whose endpoints are the center of the circle and a point on the circle • All radii of a circle are congruent!

7. Two circles are congruent if they have the same radius.

8. Chord • A segment whose endpoints lie on a circle

9. Diameter Diameter • The distance across the circle, through the center • The diameter is twice the radius

10. A diameter is a chord of a circle.

11. Secant Secant • A line that intersects a circle in two points. • It goes through the circle!

12. tangent • A line in the plane of a circle that intersects the circle in exactly one point, called the point of tangency.

13. Tangent Line Point of Tangency

14. Circle P Chord Diameter P Secant

15. Common tangent • A line or segment that is tangent to two coplanar circles

16. A B Common internal tangent • Intersects the segment that joins the centers of two circles

17. B A Common external tangent • Does NOT intersect the segment that joins the centers of two circles.

18. In a plane, two circles can intersect in two points, one point, or no points.

19. two points of intersection:

20. One point of intersection:

21. One point of intersection:

22. no points of intersection:

23. Concentric circles • Circles that lie in the same plane and have the same center