In the diagram of C, QR = ST = 16. Find CU.

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Presentation transcript:

In the diagram of C, QR = ST = 16. Find CU. EXAMPLE 4 Use Theorem 10.6 In the diagram of C, QR = ST = 16. Find CU. SOLUTION Chords QR and ST are congruent, so by Theorem 10.6 they are equidistant from C. Therefore, CU = CV. CU = CV Use Theorem 10.6. 2x = 5x – 9 Substitute. x = 3 Solve for x. So, CU = 2x = 2(3) = 6.

GUIDED PRACTICE for Example 4 In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length. 6. QR SOLUTION Since CU = CV. Therefore Chords QR and ST are equidistant from center and from theorem 10.6 QR is congruent to ST QR = ST Use Theorem 10.6. QR = 32 Substitute.

GUIDED PRACTICE for Example 4 In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length. 7. QU SOLUTION Since CU is the line drawn from the center of the circle to the chord QR it will bisect the chord. 2 So QU = QR 1 2 So QU = (32) 1 Substitute. QU = 16

GUIDED PRACTICE for Example 4 In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length. 8. The radius of C SOLUTION Join the points Q and C. Now QUC is right angled triangle. Use the Pythagorean Theorem to find the QC which will represent the radius of the C

GUIDED PRACTICE for Example 4 In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length. 8. The radius of C SOLUTION So QC2 = QU2 + CU2 By Pythagoras Theorem So QC2 = 162 + 122 Substitute So QC2 = 256 + 144 Square So QC2 = 400 Add So QC = 20 Simplify ANSWER The radius of C = 20