1. PA and PB are tangent to C. Use the figure for Exercises 1–3.
Tangent Lines
Lesson 12-1
Lesson Quiz .
PA and PB are tangent to C. Use the figure for Exercises 1–3.
1. Find the value of x.
2. Find the perimeter of quadrilateral PACB.
3. Find CP.
HJ is tangent to A and to B. Use the figure for
Exercises 4 and 5.
4. Find AB to the nearest tenth.
5. What type of special quadrilateral is AHJB? Explain
how you know.
87.2
82 cm
29 cm . .
20.4 cm
Trapezoid; the tangent line forms right angles at vertices H and J, so HA || JB.
Because HA = JB, AHJB is not a parallelogram but a trapezoid. /
12-2

2. Find the value of each variable. Leave your answer in simplest
Chords and Arcs
Lesson 12-2
Check Skills You’ll Need
(For help, go to Lesson 8-2.)
Find the value of each variable. Leave your answer in simplest
radical form.
Check Skills You’ll Need
12-2

3. A segment whose endpoints are on a circle is called a chord.
Chords and Arcs
Lesson 12-2
Notes
A segment whose endpoints are on a circle is called a chord.
12-2

4. Chords and Arcs
Lesson 12-2
Notes
12-2

5. Chords and Arcs
Lesson 12-2
Notes
12-2

6. Chords and Arcs
Lesson 12-2
Notes
12-2

7. Chords and Arcs
Lesson 12-2
Notes
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8. Chords and Arcs
Lesson 12-2
Notes
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9. Chords and Arcs
Lesson 12-2
Notes
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10. Chords and Arcs
Lesson 12-2
Notes
12-2

11. In the diagram, radius OX bisects AOB. What can you conclude?
Chords and Arcs
Lesson 12-2
Additional Examples
Using Theorem 12-4
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.
Quick Check
12-2

12. QS = QR + RS Segment Addition Postulate
Chords and Arcs
Lesson 12-2
Additional Examples
Using Theorem 12-5
Find AB.
QS = QR + RS Segment Addition Postulate
QS = 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
12-2

13. Using Diameters and Chords
Chords and Arcs
Lesson 12-2
Additional Examples
Using Diameters and Chords
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 = PQ A diameter that is perpendicular to
a chord bisects the chord. 1 2
PM = (16) = 8 Substitute. 1 2
OP 2 = PM 2 + OM 2 Use the Pythagorean Theorem.
r 2 = Substitute.
r 2 = Simplify.
r = 17 Find the square root of each side.
Quick Check
The radius of O is 17 in. .
12-2

15. For Exercises 1–5, use the diagram of L.
Chords and Arcs
Lesson 12-2
Lesson Quiz
For Exercises 1–5, use the diagram of L.
1. If YM and ZN are congruent chords, what can you conclude?
2. If YM and ZN are congruent chords, explain why you cannot
conclude that LV = LC.
3. Suppose that YM has length 12 in., and its distance from
point L is 5 in. Find the radius of L to the nearest tenth.
For Exercises 4 and 5, suppose that LV YM, YV = 11 cm, and
L has a diameter of 26 cm.
4. Find YM.
5. Find LV to the nearest tenth. .
YM ZN; YLM ZLN
You do not know whether LV and LC are perpendicular to the chords.
7.8 in.
22 cm
6.9 cm
12-2

16. hypotenuse divided by 2 : = • = , or 5.5 2
Chords and Arcs
Lesson 12-2
Check Skills You’ll Need
Solutions
1. The triangle is a 45°-45°-90° triangle, so each leg is the length of the
hypotenuse divided by 2 : = • = , or
2. The triangle is a 45°-45°-90° triangle, so each leg is the length of the
hypotenuse divided by 2: = 5
3. The triangle is a 30°-60°-90° triangle, so the hypotenuse is twice the
length of the side opposite the 30° angle: 2(14) = 28 11 2 11 2 2 2
5 2 2
12-2