Chords, Secants, and Tangents

1. Chords, Secants, and Tangents 10.1 & 10.3

2. Chord • A chord is a segment whose endpoints are on a circle. • A diameter is a chord that contains the center of the circle.

3. Secant • A secant is a line that intersects a circle in two points. • A tangent is a line that intersects the circle in exactly one point. Tangent

4. Chords, Secants, and Tangents Chord Secant Tangent

5. Common Tangents • A line, ray, or segment that is tangent to two coplanar circles is called a common tangent.

6. Theorem 10.1 • In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its intersection on the circle.

7. Using Tangent Lines

8. Theorem 10.2 • Tangent segments from a common external point are congruent.

10. Theorem 10.3 • In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

11. Theorem 10.4 • If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.

12. Theorem 10.5 • If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

13. What is the measure of Arc CD in the figure below?

14. Theorem 10.6 • In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

15. What is the value of x for the circle below?

16. Assignment • P. 655 #3-10, 18-26 • P. 667 #3-19 odds