Transcript Chords and Arcs LESSON 12-2 Additional Examples In the diagram, radius OX bisects can you conclude? AOX AOB.

Chords and Arcs
LESSON 12-2
Additional Examples
In the diagram, radius OX bisects
can you conclude?
AOX
AOB. What
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.
Quick Check
HELP
GEOMETRY
Chords and Arcs
LESSON 12-2
Additional Examples
Find AB.
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.
Quick Check
HELP
GEOMETRY
Chords and Arcs
LESSON 12-2
Additional Examples
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.
PM =
1
PQ
2
PM = 1 (16) = 8
2
OP 2 = PM 2 + OM 2
r 2 = 82 + 152
r 2 = 289
r = 17
The radius of . O is 17 in.
HELP
A diameter that is perpendicular to
a chord bisects the chord.
Substitute.
Use the Pythagorean Theorem.
Substitute.
Simplify.
Find the square root of each side.
Quick Check
GEOMETRY