10.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply Properties of Chords.

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Presentation transcript:

10.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply Properties of Chords

10.3 Warm-Up ANSWER radius 1.DC Tell whether the segment is best described as a radius, chord, or diameter of C. ANSWER diameter 2.BD

10.3 Warm-Up Tell whether the segment is best described as a radius, chord, or diameter of C. ANSWER chord 3.DE ANSWER chord 4.AE

10.3 Warm-Up 5. Solve 4x = 8x – Solve 3x + 2 = 6x – 4. ANSWER 3 2

10.3 Example 1 In the diagram, P Q, FG JK, and mJK = 80 o. Find mFG. SOLUTION Because FG and JK are congruent chords in congruent circles, the corresponding minor arcs FG and JK are congruent. So, mFG = mJK = 80 o.

10.3 Guided Practice Use the diagram of D. 1. If mAB = 110°, find mBC. mBC = 110° ANSWER 2. If mAC = 150°, find mAB mAB = 105° ANSWER

10.3 Example 2 SOLUTION STEP 1 Label the bushes A, B, and C, as shown. Draw segments AB and BC. Three bushes are arranged in a garden as shown. Where should you place a sprinkler so that it is the same distance from each bush? Gardening

10.3 Example 2 STEP 2 Draw the perpendicular bisectors of AB and BC By Theorem 10.4, these are diameters of the circle containing A, B, and C. STEP 3 Find the point where these bisectors intersect. This is the center of the circle through A, B, and C, and so it is equidistant from each point.

10.3 Example 3 Use the diagram of E to find the length of AC. Tell what theorem you use. Diameter BD is perpendicular to AC. So, by Theorem 10.5, BD bisects AC, and CF = AF. Therefore, AC = 2 AF = 2(7) = 14. SOLUTION

10.3 Guided Practice 3. CD Find the measure of the indicated arc in the diagram. 72° ANSWER 4. DE5. CE 72° ANSWER 144° ANSWER

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

10.3 Guided Practice 6. QR In the diagram in Example 4, suppose ST = 32, and CU = CV = 12. Find the given length. 32 ANSWER 7. QU 16 ANSWER 16 ANSWER 8. The radius of C

10.3 Lesson Quiz 1. Find the value of x in C. Explain.. ANSWER 6 ; If a diameter of a circle is to the chord, then the diameter bisects the chord and its arc.

10.3 Lesson Quiz Find the value of x in C. Explain.. 2. ANSWER 4 ; In the same circle, if two chords are equidistant from the center, then they are. = ~

10.3 Lesson Quiz 3. Determine whether RS is a diameter. ANSWER Yes. Sample answer: RS is the bisector of TU by Theorem 5.3. Then RS is a diameter of the circle by Theorem 10.4.