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Find Segment Lengths in Circles

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Presentation on theme: "Find Segment Lengths in Circles"— Presentation transcript:

1 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Theorem 6.16 Segments of Chords 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. B A C D E

2 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Example 1 Find lengths using Theorem 6.16 Find ML and JK. K M L J N Find ML and JK by substitution.

3 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Theorem 6.17 Segments of Secants If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. B A C D E

4 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Example 2 Find lengths using Theorem 6.17 Find the value of x. Q R P S T Solution 6.17 Use Theorem _____ Substitute. Simplify. Solve for x.

5 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Checkpoint. Find the value of x.

6 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Checkpoint. Find the value of x.

7 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Theorem 6.18 Segments of Secants and Tangents If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment. E A C D

8 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Example 3 Find lengths using Theorem 6.18 Find RS. Q S R T Solution 6.18 Use Theorem _____ Substitute. Simplify. Write in standard form. Use quadratic formula.

9 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Example 3 Find lengths using Theorem 6.18 Find RS. Q S R T Solution Simplify. Lengths cannot be __________, so use the _________ solution. negative positive So, x = ___________

10 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Checkpoint. Complete the following exercise. M J K L

11 Find Segment Lengths in Circles
6.6 Find Segment Lengths in Circles Pg. 231, 6.6 #1-24

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