Incenter and Circumcenter Answers

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Which statements must be true regarding the diagram?

A
BG ≅ AG
B
DG ≅ FG
C
DG ≅ BG
D
GE bisects ∠DEF
E
GA bisects ∠BAF
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insideonoutside

A
inside
B
on
C
outside
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insideonoutside

A
inside
B
on
C
outside
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insideonoutside

A
inside
B
on
C
outside
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insideonoutside

A
inside
B
on
C
outside
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Which statements must be true regarding the diagram?

A
∠HDC ≅ ∠HDE
B
AB ≅ AF
C
AB ≅ BC
D
HC ≅ HE
E
HA ≅ HB
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What is SU?

A
SU = 5
B
SU = 7
C
SU = 12
D
SU = 13
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Which triangle shows the incenter at point A?

A
[Image: Point A is inside of a triangle. Lines are drawn f...]
B
[Image: Point A is inside of a triangle. Lines are drawn f...]
C
[Image: Point A is inside of a triangle. Lines are drawn f...]
D
[Image: Point A is inside of a triangle. Lines are drawn f...]
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What does point P represent with regard to the triangle?

A
the point of concurrency of the altitudes
B
the point of concurrency of the angle bisectors
C
the point of concurrency of the medians
D
the point of concurrency of the perpendicular bisectors
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What is the length of Line segment H A ?

Question illustration
A
7 units
B
8 units
C
24 units
D
48 units
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Three highways connect the centers of three towns and form a triangle. A cell phone company wants to place a new cell tower so that it is the same distance from the centers of the three towns. How can the company find where to place the tower? Explain.

Answer:

The company should place the tower at the circumcenter of the triangle formed by the three towns. The circumcenter is the point that is equidistant from the vertices (the towns). To find this point, the company needs to construct the perpendicular bisectors of the three sides of the triangle; the point where these bisectors intersect is the location for the tower.

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What did you include in your response? Check all that apply.

A
The tower needs to be equidistant from the vertices of the triangle.
B
The tower should be placed at the circumcenter of the triangle.
C
To find the circumcenter, find the intersection point of the three perpendicular bisectors of the triangle.

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