Answers25-26 IHS Geometry A-CRTriangle Angle Theorems

Incenter and Circumcenter Answers

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1
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In the diagram, Z is the circumcenter of triangle TUV.

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A
2 units
B
6 units
C
8 units
D
10 units
2
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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.
3

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.
4

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
5

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.
6

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
7

The figure shows a circle circumscribed around a triangle.

Question illustration
A
perpendicular segments to the vertices of the triangle
B
perpendicular bisectors of the sides of the triangle
C
angle bisectors of each angle of the triangle
D
the incenter of the triangle
8

Point O is the incenter of triangle ABC.

Question illustration
A
30°
B
60°
C
75°
D
90°
9

Point A is the incenter of ΔDEF.

Question illustration
A
2 units
B
9 units
C
11 units
D
14 units
10

Point X is the circumcenter of ΔABC.

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

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