Preparing for the Regents Examination Geometry, AK

3. mCDB 1 _ m (
2 CB )
4. mE mCDB
5. CBD FCE (AA)
6. EF _ EC
CD _
DB (Corresponding
sides of similar
triangles are in
proportion.)
14 1. AZT MZH
2. HMT TAH
3. MZH AZT (AA)
4. MZ _
AZ
ZH _
ZT (Corresponding
sides of similar
triangles are in
proportion.)
15 a 1. BAC BDC
2. ABD ACD
(Congruent inscribed
angles)
3. ACD ABE
b BE 6
(AA)
13-8 Circles in the
Coordinate Plane
(pages 386–387)
1 (2) (x 4) 2 (y 3) 2 36
2 (4) (13, 1)
3 a (x 1) 2 (y 4) 2 25
b (x 3) 2 (y 2) 2 49
c (x 4) 2 (y 1) 2 121
d (x 2) 2 (y 5) 2 64
e (x 2) 2 y 2 121
f x 2 y 2 144
4 a x 2 y 2 49
b (x 4) 2 y 2 25
c x 2 y 2 41
d (x 2) 2 y 2 36
e (x 3) 2 (y 2) 2 9
f (x 1) 2 (y 3) 2 25
5 For parts a–d, check students’ graphs. The
center and radius of each circle are listed
below.
a C(2, 4), r 3
b C(3, 4), r 5
c C(0, 2), r 4
d C(6, 0), r 2
6 a C(0, 0), r 9
b C(0, 0), r 11
c C(0, 0), r 20
d C(0, 0), r 1
e C(0, 0), r √ 2
7 Note: Students’ answers may vary for the
two other points on the circle.
a C(5, 3), r 8; (5, 11), (5, 5)
b C(4, 0), r 10; (6, 0), (14, 0)
c C(2, 5), r 4; (2, 5), (6, 5)
d C(3, 7), r 2 √ 3 ; (3, 7 2 √ 3 ),
(3, 7 2 √ 3 )
8 a x 2 y 2 25
b x 2 y 2 4
c x 2 y 2 34
d x 2 y 2 37
e x 2 y 2 68
9 a (x 2) 2 (y 3) 2 2
b (x 3) 2 (y 7) 2 80
10 a x 2 (y 0.5) 2 12.25
b (x 3) 2 (y 3) 2 5
11 a Circumference 8, area 16
b Circumference 12, area 36
c Circumference 2 √ 13 , area 13
12 a (3, 0)
b (x 3) 2 (y 1) 2 1
c
13 a C(1, 3), r 2 √ 2
b Area 8, circumference 4 √ 2
13-9 Tangents, Secants,
and the Circle in the
Coordinate Plane
(pages 392–393)
1 (1) 0
2 a (3, 11), (3, 1)
b (3) x 1
3 y 0
4 y 0.5x 2.5
5 y x 4
6 y 3
7 y 4
8 y 2x 10
9 a (4, 3), (3, 4) b secant
10 a (0, 4), (4, 0) b secant
11 a (2, 3), (2, 5) b secant
12 a (0, 3) b tangent
13 a (0, 2), (2, 0) b secant
14 a (5, 5) b tangent
15 a (1, 4), (1, 4) b secant
13-9 Tangents, Secants, and the Circle in the Coordinate Plane 85