Preparing for the Regents Examination Geometry, AK

13-2 Arcs and Chords
(pages 350–351)
1 a 16 b 7.5 c m _
d 3 √ 6 e 5 √ 2
2
2 a True
3 109
b True c False
4 a 90 b 72 c 60 d 36
5 a 24 b 22.5 c 20
d 18 e 15
6 a 10 b 5 √ 2 c 5
7 a 6
8 6 in.
9 17
b 6 √ 2 c 12 d 6 √ 2
10 a 15
11 6.
12 8 √ 2
13 x √ 2
14 5
15 25
b 7.5
16 a 30 b 60 c 60
d 60 e 60 f 300 g 150
17 a 30 b 60 c 10
d 5 e 5 √ 3
Note: Since there are many variations of proofs,
the following is simply one set of acceptable
statements to complete each proof. Depending
on the textbook used, the wording and format
of reasons may differ, so they have not been
supplied for the method of congruence applied
in each problem. (These solutions are intended
to be used as a guide—other possible solutions
may vary.)
18 1. Radii −−−
OK and −−−
OM
2. AOL DOL (Central angles are
congruent.)
3. −−
LA −−−
OK , −−
LD −−−
OM
4. LAO and LDO are right angles.
5. LAO and LDO are right triangles.
6. LAO LDO
7. −−
LO −−
LO
8. LAO LDO (Leg-angle)
19 1. ABD CBD
2. −−−
OA −−
OB
3. BAO ABD
4.
(All radii of the
same circle are
congruent.)
−−−
OC −−
OB
5. BCO CBD
80 Chapter 13: Geometry of the Circle
6. AOB COB
7. AOD COD
8. AD CD (Congruent inscribed
angles intercept congruent
arcs.)
20 1. −−−
OA , −−
OB , and −−−
OC are radii of circle O.
2. BAC BCA
3. AB BC (Congruent inscribed
angles intercept congruent
arcs.)
4. AOB COB (Central angles are
equal to their arcs.)
13-3 Inscribed Angles
and Their Measure
(pages 354–357)
1 a 25 b 55 c 125
d 60.4 e 4
2 a 52 b 124 c 15
d 180 e (16x)
3 mx 70, my 35; 70 35 105
4 a 50 b 130 c 56
d 25
5 53
6 70
7 80
8 35
9 140
e 62 f 25
10 mC 75, mM 82
11 85.5
12 m 1 120, m2 45, m3 75, m4 60
13 m1 57, m2 33, m3 90, m 4 114
14 m 1 74, m 2 74, m3 37, m4 106
15 a 140 b 80 c 40
d 70 e 70
16 m1 57, m2 48, m3 57, m4 48
17 a 80 b 188 c 46 d 94
18 a 64 b 108 c 140 d 70
e 24 f 54 g 94
19 a 86 b 102 c 88
d 56 e 116
20 a 44 b 88 c 44 d 44
e 92 f 88
21 a 60 b 60 c 60 d 30
e 60 f 120 g 30 h 60
i 120 j 60 k 90 l 30