Find Segment Lengths in Circles

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Presentation transcript:

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

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.

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

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.

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

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

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

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.

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 = ___________

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

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