Name
Class
Date
Practice
5-3
Form K
Bisectors in Triangles
Coordinate Geometry Find the coordinates of the circumcenter of
each triangle.
y
1.
2.
(2, 2.5)
4
4
y
(1, 3)
2
x
x
O
2
2
4
O
2
4
2
Coordinate Geometry Find the circumcenter of kPQR.
3. P (0, 0) (1.5, 2)
y R
To start, graph the vertices and connect
them on a coordinate plane. Then draw
two perpendicular bisectors.
Q (3, 4)
R (0, 4)
Q
2
x
O P
2
2
4
2
4. P (1, 25) (2.5, 23.5)
5. P (23, 25) (21, 21.5)
Q (4, 25)
Q (23, 2)
R (1, 22)
R (1, 25)
6. P (26, 6) (21.5, 4)
7. P (4, 6) (2.5, 2)
Q (3, 6)
Q (1, 6)
R (26, 2)
R (1, 22)
8
y
X
6
8. a. Which point is equidistant from the three posts? Y
Y
4
b. Where are the coordinates of this point? (3, 5)
2
Post A
Z
Post B
Post C
O
2
x
4
6
8
A
9. Construction Construct three perpendicular
bisectors for nABC. Then use the point of
concurrency to construct the circumscribed circle.
C
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B
Name
Class
Date
Practice (continued)
5-3
Form K
Bisectors in Triangles
Name the point of concurrency of the angle bisectors.
B Q
10.
A
R
E
11.
P
S
S
Q
U
T
D
C
12.
N
W
X
Y
X
J
L
F
V
13.
K X
U
M
Z
B
Z
A
O
V
Find the value of x.
4
14. To start, identify the relationship between the
line segments that are labeled.
Because the segments meet at the point where
the 9 meet, the segments are 9.
2x 4
3x
angle bisectors; congruent
Then write an equation to find x:
z
3x
z5z
2x
z1z
15.
4
z
16.
2
11
x 13
x 9
3x 5
2x 2
17. Construction Construct two angle bisectors for nXYZ.
Then use the point of concurrency to construct the
inscribed circle.
Y
X
Z
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