Name
Class
Date
Practice
5-3
Form G
Bisectors in Triangles
Coordinate Geometry Find the circumcenter of each triangle.
1.
2.
y
4
3.
y
2
y
x
O
4
2
x
2
O
4
2
4
x
3
6
(3.5, 2)
2 O
4
(0, 22)
(22, 2)
Coordinate Geometry Find the circumcenter of kABC.
4. A(1, 3) (2.5, 2.5)
5. A(2, 23) (21, 25)
7. A(5, 6) (2.5, 1.5)
6. A(25, 22) (22, 2)
B(4, 3)
B(24, 23)
B(1, 22)
B(0, 6)
C(4, 2)
C(24, 27)
C(1, 6)
C(0, 23)
8. A(1, 3) (3, 2.5)
9. A(2, 22) (21, 24.5) 10. A(25, 23) (22, 1.5) 11. A(5, 2) (2, 20.5)
B(5, 3)
B(24, 22)
B(1, 23)
B(21, 2)
C(5, 2)
C(24, 27)
C(1, 6)
C(21, 23)
Name the point of concurrency of the angle bisectors.
12. M
B
P
P
A
13.
G
N
A
H
B
R
C
D
W
V
16. Q
F
F
H
E
C
D
S
X
U
T
N
O
N
G
A
W
F
O
15.
14. Q
B
I J
E
C
I
P
M
N
17.
R
R
S
M
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T
P
S
P
Q
O
Name
Class
Date
Practice (continued)
5-3
Form G
Bisectors in Triangles
Find the value of x.
3
18.
5
20.
3x
2x 5
x3
2x
5
19.
x2
2x 3
21.
2.5
22.
21
0.25
23.
x8
5x 4
x5
3x 7
24. Where should the farmer place the
25. Where should the fire station be
hay bale so that it is equidistant from
the three gates? (0, 1.6)
Gate C
Gate A
Police station
2
y
4
2
x
Gate B
4
placed so that it is equidistant
from the grocery store, the
hospital, and the police station? (1, 1)
y
6
5x 7
x6
O
2
x
4
4
O
4
Grocery store
Hospital
26. Construction Construct three
27. Construction Construct two
perpendicular bisectors for nLMN .
Then use the point of concurrency to
construct the circumscribed circle.
angle bisectors for nABC. Then
use the point of concurrency to
construct the inscribed circle.
N
B
A
L
M
C
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24