GeometryGeometry

AOX BOX by the definition of an angle bisector.

Lesson 12-2

Chords and ArcsChords and Arcs

In the diagram, radius OX bisects AOB. What can you conclude?

AX BX because congruent central angles have congruent chords.

AX BX because congruent chords have congruent arcs.

Additional Examples

GeometryGeometry

QS = QR + RS Segment Addition Postulate

QS = 7 + 7 Substitute.

QS = 14 Simplify.

AB = QS Chords that are equidistant from the center of a circle are congruent.

AB = 14 Substitute 14 for QS.

Find AB.

Lesson 12-2

Chords and ArcsChords and Arcs

Additional Examples

GeometryGeometry

OP 2 = PM

2 + OM 2 Use the Pythagorean Theorem.

r 2 = 82 + 152 Substitute.r 2 = 289 Simplify.r = 17 Find the square root of each side.

PM = PQ A diameter that is perpendicular to a chord bisects the chord.

12

PM = (16) = 8 Substitute.12

The radius of O is 17 in..

Draw a diagram to represent the situation. The distance from the center of O to PQ is measured along a perpendicular line.

.

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.

..

Lesson 12-2

Chords and ArcsChords and Arcs

Additional Examples