1. LESSON F: Segment Lengths in Circles During this lesson, you will find the lengths of segments of chords, tangents and secants in circles.

2. PART I: FINDING THE LENGTHS OF SEGMENTS OF CHORDS When two chords intersect in the interior of a circle, each chord is divided into two segments which are called______________________.. segments of a chord THEOREM If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Name two segments of each chord in the diagram below:

3. EXAMPLE 1 Finding Segment Lengths Chords ST and PQ intersect inside the circle. Find the value of x. RQ * XP = SR * RT 9 * x = 3 * 6 9x = 18 x = 2

4. PART II: USING SEGMENTS OF TANGENTS AND SECANTS THEOREM If two tangents share the same endpoint outside a circle, then the product of the length of one secant segment and the length of its external secant segment equals the product of the length of the other secant segment and the length of its external secant segment.

5. If a secant and a tangent segment share an endpoint outside a circle, then the product of the sum of the length of the secant segment and the length of its external segment equals the square of the tangent segment. THEOREM

6. EXAMPLE 2 Finding Segment Lengths Find the value of x. RP * RQ = RS * ST 9 * 20 = 10* ( X +10) 180 = 10X + 100 80 = 10X X = 8

7. EXAMPLE 3 Estimating the Radius of a Circle You are standing at point C, about 8 feet from a circular aquarium tank. The distance from you to a point of tangency on the tank is about 20 feet. Estimate the radius of the tank. The Caribbean Coral Reef Tank at the New England Aquarium is a circular tank 24 feet deep.

8. Work Space: (CB) 2 = CE * (2r + 8) (20) 2 = 8 * (2r + 8) 400 = 16r + 64 336 = 16r 21 ≈ r Example 4 Finding Segment Lengths

9. 15,: 18: 12 12;15; 50x + 8; 4 2; 6 9;6x + 3; x 2 ; 1

10. Homework Assignment: Segment Lengths WS