AnswersMO-Geometry AIncenter and Circumcenter

Incenter and Circumcenter Answers

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Three friends want to meet at a place that is the same distance from each of their houses. They draw a map and measure the approximate distances and angles, as shown.

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A
Find the midpoint of the segments which connect their houses.
B
Bisect each of the angles with vertices at their houses.
C
Draw perpendicular lines through any point on the segments which connect their houses.
D
Draw perpendicular line segments from each vertex to the opposite side.
2
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Which must be true? Select three options

A
Point A is the center of the circle that passes through points D, E, and F.
B
Point A is the center of the circle that passes through points X, Y, and Z.
C
Line segment Z A is-congruent-to line segment Y A
Option C
D
Line segment E A is-congruent-to line segment F A
Option D
E
Line segment A X is-congruent-to line segment A Y
Option E
3

Point O is the incenter of triangle ABC.

Question illustration
A
30°
B
60°
C
75°
D
90°
4

Point A is the incenter of ΔDEF.

Question illustration
A
7
B
11
C
14
D
15
5

Point A is inside triangle E D F. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A L, A M, and A N. The length of A E is 10 and the length of A D is 2 n + 4.

Question illustration
A
2
B
3
C
4
D
5
6

Point X is the circumcenter of ΔABC.

Question illustration
A
1.5 cm
B
2 cm
C
2.5 cm
D
3 cm
7

Point G is the incenter of the triangle.

Question illustration
A
4
B
8
C
24
D
32
8

Point Y is the circumcenter of triangle DEF.

Question illustration
A
Point Y is the center of the circle that passes through points D, F, and N.
B
Point Y is the center of the circle that passes through points M, N, and E.
C
Point Y is the center of the circle that passes through points L, M, and N.
D
Point Y is the center of the circle that passes through points D, E, and F.
9

Point H is the circumcenter of ΔJKL.

Question illustration
A
Line segment F H is-congruent-to line segment D H
Option A
B
Line segment J F is-congruent-to line segment L H
Option B
C
Line segment J H is-congruent-to line segment L H
Option C
D
Line segment K F is-congruent-to line segment L D
Option D
10

Point P is the incenter of ΔRST.

Question illustration
A
Line segment C P is-congruent-to line segment R P
Option A
B
Line segment B P is-congruent-to line segment P C
Option B
C
PSC PTC
Option C
D
BPS APT
Option D

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