Segment Lengths in Circles

1. Segment Lengths in Circles Mrs. Rawat

2. Theorem When chords intersect, the chords break into segments that are equal when multiplied.

3. Theorem When chords intersect, the chords break into segments that are equal when multiplied.

4. Theorem When chords intersect, the chords break into segments that are equal when multiplied.

5. Theorem When chords intersect, the chords break into segments that are equal when multiplied.

6. Theorem When two secants intersect a circle, the segments of the secants (the chord and the whole secant ) are equal when multiplied together.

7. Theorem When two secants intersect a circle, the segments of the secants (the chord and the whole secant ) are equal when multiplied together.

8. Theorem When two secants intersect a circle, the segments of the secants (the chord and the whole secant ) are equal when multiplied together.

9. Theorem A tangent and a secant

10. Theorem A tangent and a secant

11. Theorem A tangent and a secant

12. Theorem A tangent and a secant

14. HK and HG are tangent to F. Find HG. Example 4: Using Properties of Tangents 2 segments tangent to from same ext. point segments . HK = HG 5a – 32 = 4 + 2a Substitute 5a – 32 for HK and 4 + 2a for HG. 3a –32 = 4 Subtract 2a from both sides. 3a = 36 Add 32 to both sides. a = 12 Divide both sides by 3. HG = 4 + 2(12) Substitute 12 for a. = 28 Simplify.

15. RS and RT are tangent to Q. Find RS. Substitute for RS and x – 6.3 for RT. x 4 Check It Out! Example 4a 2 segments tangent to from same ext. point segments . RS = RT x = 4x – 25.2 Multiply both sides by 4. –3x = –25.2 Subtract 4x from both sides. x = 8.4 Divide both sides by –3. Substitute 8.4 for x. = 2.1 Simplify.