the point where the angle bisectors of a triangle intersect is called the
the point where the perpendicular bisectors of a triangle intersect is called the
the incenter is equidistant from all
of the triangle.
the circumcenter is equidistant from all
of the triangle.
the circle that passes through all the vertices of a triangle is called the
the circle that is tangent to all sides of a triangle is called the
the perpendicular bisectors of a triangle are used to find the
the angle bisectors of a triangle are used to find the
in a right triangle, the circumcenter is located at the
of the hypotenuse.
the incenter is always located
the triangle.
the circumcenter of an obtuse triangle is located
the triangle.
the incenter is the center of the
of a triangle.
the circumcenter is the center of the
of a triangle.
the
is the point where the medians of a triangle intersect
the
is the point where the altitudes of a triangle intersect.

Question

Accepted Answer

### 1. The point where the angle bisectors of a triangle intersect is called the
# Brief Explanations:
In triangle geometry, the intersection of angle bisectors is defined as the incenter, which is the center of the incircle (tangent to all sides).
# Answer:
incenter

### 2. The point where the perpendicular bisectors of a triangle intersect is called the
# Brief Explanations:
Perpendicular bisectors of a triangle meet at the circumcenter, the center of the circumcircle (passing through all vertices).
# Answer:
circumcenter

### 3. The incenter is equidistant from all ______ of the triangle.
# Brief Explanations:
The incenter’s property is equal distance to all sides of the triangle (since it is the center of the incircle, tangent to each side).
# Answer:
sides

### 4. The circumcenter is equidistant from all ______ of the triangle.
# Brief Explanations:
The circumcenter is equidistant from all vertices of the triangle (as it is the center of the circumcircle passing through all vertices).
# Answer:
vertices

### 5. The circle that passes through all the vertices of a triangle is called the
# Brief Explanations:
A circle passing through all three vertices of a triangle is the circumcircle, with its center at the circumcenter.
# Answer:
circumcircle

### 6. The circle that is tangent to all sides of a triangle is called the
# Brief Explanations:
A circle tangent to all three sides of a triangle is the incircle, centered at the incenter.
# Answer:
incircle

### 7. The perpendicular bisectors of a triangle are used to find the
# Brief Explanations:
Perpendicular bisectors intersect at the circumcenter, so they are used to locate the circumcenter (and circumcircle).
# Answer:
circumcenter

### 8. The angle bisectors of a triangle are used to find the
# Brief Explanations:
Angle bisectors intersect at the incenter, so they are used to locate the incenter (and incircle).
# Answer:
incenter

### 9. In a right triangle, the circumcenter is located at the ______ of the hypotenuse.
# Brief Explanations:
In a right triangle, the hypotenuse is the diameter of the circumcircle, so the circumcenter lies at the midpoint of the hypotenuse.
# Answer:
midpoint

### 10. The incenter is always located ______ the triangle.
# Brief Explanations:
The incenter, being the intersection of angle bisectors, always lies inside the triangle (as angle bisectors of a triangle stay within the triangle).
# Answer:
inside

### 11. The circumcenter of an obtuse triangle is located ______ the triangle.
# Brief Explanations:
For an obtuse triangle, the circumcenter lies outside the triangle (since the perpendicular bisectors of the longest side extend outside the triangle’s interior).
# Answer:
outside

### 12. The incenter is the center of the ______ of a triangle.
# Brief Explanations:
The incenter is the center of the incircle, which is tangent to all three sides of the triangle.
# Answer:
incircle

### 13. The circumcenter is the center of the ______ of a triangle.
# Brief Explanations:
The circumcenter is the center of the circumcircle, which passes through all three vertices of the triangle.
# Answer:
circumcircle

### 14. The ______ is the point where the medians of a triangle intersect.
# Brief Explanations:
Medians of a triangle (segments from vertices to midpoints of opposite sides) intersect at the centroid.
# Answer:
centroid

### 15. The ______ is the point where the altitudes of a triangle intersect.
# Brief Explanations:
Altitudes (perpendicular segments from vertices to opposite sides) intersect at the orthocenter.
# Answer:
orthocenter

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QUESTION IMAGE

Question

Explanation:

1. The point where the angle bisectors of a triangle intersect is called the

Answer:

2. The point where the perpendicular bisectors of a triangle intersect is called the