Chapter 10.3 Notes: Apply Properties of Chords

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Presentation transcript:

Chapter 10.3 Notes: Apply Properties of Chords Goal: You will use relationships of arcs and chords in a circle.

Any chord divides the circle into two arcs. What is a chord? A chord is a segment with endpoints on a circle. Any chord divides the circle into two arcs. A diameter divides a circle into two semicircles. Any other chord divides a circle into a minor arc and a major arc.

Theorem 10.3: In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. Ex.1: In the diagram, and Find

Ex.2: Use the diagram of a. If find b. If find

Bisecting Arcs Theorem 10.4: If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. Theorem 10.5: If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

Ex.3: Use the diagram of to find the length of Tell what theorem you used. Ex.4: Find the measure of the indicated arc. a. b. c.

Theorem 10.6: In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center. Ex.5: In the diagram of QR = ST = 16. Find CU.

Ex. 6: In the diagram in example 5, suppose ST = 32, and CU = CV = 12 Ex.6: In the diagram in example 5, suppose ST = 32, and CU = CV = 12. Find the given length. a. QR b. QU c. the radius of

Ex.7: Use the diagram of to find the length of Tell what theorem you used. Ex.8: In the diagram of PV = PW, QR = 2x + 6, and ST = 3x – 1. Find QR.

Ex.9: In and Find