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Chords and Arcs

In the diagram, radius OX bisects AOB . What can you conclude?. AOX BOX by the definition of an angle bisector. AX BX because congruent central angles have congruent chords. AX BX because congruent chords have congruent arcs. Chords and Arcs. Lesson 12-2.

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Chords and Arcs

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  1. In the diagram, radius OX bisects AOB. What can you conclude? AOXBOX by the definition of an angle bisector. AX BX because congruent central angles have congruent chords. AX BX because congruent chords have congruent arcs. Chords and Arcs Lesson 12-2 Additional Examples

  2. Find AB. Chords and Arcs Lesson 12-2 Additional Examples QS = QR + RSSegment Addition Postulate QS = 7 + 7 Substitute. QS = 14 Simplify. AB = QSChords that are equidistant from the center of a circle are congruent. AB = 14 Substitute 14 for QS.

  3. . . . . P and Q are points on O. The distance from O to PQ is 15 in., and PQ = 16 in. Find the radius of O. Draw a diagram to represent the situation. The distance from the center of O to PQ is measured along a perpendicular line. 1 2 PM = PQ A diameter that is perpendicular to a chord bisects the chord. 1 2 PM = (16) = 8 Substitute. The radius of O is 17 in. Chords and Arcs Lesson 12-2 Additional Examples OP2 = PM2 + OM2Use the Pythagorean Theorem. r 2 = 82 + 152Substitute. r 2 = 289 Simplify. r = 17 Find the square root of each side.

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