Incenter and Circumcenter Answers

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1
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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
2
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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.
108349

Where do the points of concurrency of certain types of triangles lie?

Answers:
The circumcenter of an obtuse triangle lies the triangle.:outside
The incenter of a right triangle lies the triangle.:inside
The point of concurrency of the angle bisectors of an acute triangle lies the triangle.:inside
The point of concurrency that is equidistant from the vertices of a right triangle lies the triangle.:on
108350

insideonoutside

A
inside
B
on
C
outside
108351

insideonoutside

A
inside
B
on
C
outside
108352

insideonoutside

A
inside
B
on
C
outside
108360

Which statements must be true regarding the diagram?

A
∠HDC ≅ ∠HDE
B
AB ≅ AF
C
AB ≅ BC
D
HC ≅ HE
E
HA ≅ HB
108361

What is SU?

A
SU = 5
B
SU = 7
C
SU = 12
D
SU = 13
108362

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
108365

What is the length of Line segment H A ?

Question illustration
A
7 units
B
8 units
C
24 units
D
48 units
108366

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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insideonoutside

A
inside
B
on
C
outside

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Incenter and Circumcenter Answers — CA-Common…