1. Brain Buster 1. Draw 4 concentric circles
2. Draw an internally tangent line to two circles
3. Name two different types of segments that are equal.
4. Explain the difference between a secant & a chord
5. What do you know about a tangent line and the radius drawn to the point of tangency?

2. Arcs and
Section 10.2
Chords

3. Central Angle : An Angle whose vertex is at the center of the circle
Major Arc
Minor Arc
More than 180°
Less than 180°
ACB P AB
To name: use 3 letters C
To name: use 2 letters B
APB is a Central Angle

4. Semicircle: An Arc that equals 180°
To name: use 3 letters E D
EDF P F

5. THINGS TO KNOW AND REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal

6. measure of an arc = measure of central angle
96 Q
m AB =
96° B C
m ACB =
264°
m AE =
84°

7. Arc Addition PostulateB
m ABC =
+ m BC
m AB

8. 240 260 m DAB = m BCA = Tell me the measure of the following arcs. D
140
260
m BCA = R
40
100
80 C B

9. CONGRUENT ARCS
Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. C B D 45 45
110 A

10. In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. B C
AB  CD IFF AB  DC A D

11. 60
120
120 x
x = 60

12. 2x
x + 40
2x = x + 40
x = 40

13. *YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
IF: AD  BD and AR  BR
THEN: CD  AB C P A R D B
*YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*

14. What can you tell me about segment AC if you know it is the perpendicular bisectors of segments DB?
It’s the DIAMETER!!! A C B

15. Ex. 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
x = 24 24 y
60
y = 30 x

16. Example 2
EX 2: IN P, if PM  AT, PT = 10, and PM = 8, find AT. P A M
MT = 6 T
AT = 12

17. RZ = 8 Example 3 In R, XY = 30, RX = 17, and RZ  XY. Find RZ. X R Z

18. x = 1.5 Example 4 IN Q, KL  LZ. IF CK = 2X + 3 and CZ = 4x, find x.

19. In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. B
AD  BC
IFF
LP  PM A M P L C D

20. Ex. 5: In A, PR = 2x + 5 and QR = 3x –27. Find x.