AnswersMO-Geometry AIncenter and Circumcenter

Incenter and Circumcenter Answers

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1
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Point X is the circumcenter of ΔABC.

Question illustration
A
1.5 cm
B
2 cm
C
2.5 cm
D
3 cm
2
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Point A is the incenter of ΔDEF.

Question illustration
A
7
B
11
C
14
D
15
3

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
4

Point Y is the circumcenter of ΔDEF.

Question illustration
A
5
B
11
C
17
D
22
5

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
6

Point A is the point of concurrency of the angle bisectors of ΔDEF.

Question illustration
A
ZA = 3cm
B
ZA = 4cm
C
ZA = 5cm
D
ZA = 6cm
7

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
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

Which is the only center point that lies on the edge of a triangle?

A
the incenter of a right triangle
B
the incenter of an obtuse triangle
C
the circumcenter of a right triangle
D
the circumcenter of an obtuse triangle
10

The figure shows a circle inscribed in a triangle.

Question illustration
A
A circle was constructed using the intersection of the angle bisectors as the center of the circle and the obtuse vertex as a point on the circumference of the circle.
B
A circle was constructed using a vertex as the center of the circle and the intersection of the angle bisectors as a point on the circumference of the circle.
C
Segments perpendicular to the sides of the triangle through the intersection of the angle bisectors were constructed.
D
Segments bisecting each side of the triangle were constructed through the intersection of the angle bisectors.

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