8 how do you construct the incenter of a triangle?
a. by intersecting the angle bisectors of the triangle
b. by intersecting the medians of the triangle
c. by intersecting the perpendicular bisectors of the triangle
d. by bisecting the angles of the triangle
9 what is the point called where the perpendicular bisectors of a triangle intersect?
a. tangent
b. circumcenter
c. incenter
d. centroid
10. a radius is drawn to the midpoint of a chord. what is true about their relationship?
a. they intersect at an angle of 45°.
b. they are parallel.
c. they are perpendicular.
d. they are equal in length.
11. what is the first step to construct the centroid of a triangle?
a. draw a circle in the triangle
b. construct the angle bisectors of each angle
c. identify the midpoints of each side
d. construct the perpendicular bisectors of each side
12. what is the central angle of a sector in radians if its area is half the area of the entire circle?
a. 2π/3 radians
b. π radians
c. π/2 radians
d. 2π radians
13. what is the sector area of a circle with radius 12 cm if the central angle is π/6 radians?
a. 6π square cm
b. 12π square cm
c. 24π square cm
d. 28π square cm
14. how many radians are there in a quarter of a circle?
a. π/2 radians
b. π/3 radians
c. π/6 radians
d. π/8 radians

Question

Accepted Answer

# 8.
## Brief Explanations:
The in - center of a triangle is the point of intersection of the angle bisectors of the triangle.
# Answer:
a. By intersecting the angle bisectors of the triangle

# 9.
## Brief Explanations:
The circum - center is the point where the perpendicular bisectors of a triangle intersect.
# Answer:
b. Circum - center

# 10.
## Brief Explanations:
A radius drawn to the mid - point of a chord is perpendicular to the chord.
# Answer:
c. They are perpendicular

# 11.
## Brief Explanations:
To construct the centroid of a triangle, the first step is to identify the mid - points of each side.
# Answer:
c. Identify the mid - points of each side

# 12.
## Brief Explanations:
The area of a sector is given by $A=\frac{1}{2}r^{2}\theta$, and the area of a circle is $A = \pi r^{2}$. If the area of the sector is half of the area of the circle, then $\frac{1}{2}r^{2}\theta=\frac{1}{2}\pi r^{2}$, so $\theta=\pi$ radians.
# Answer:
b. $\pi$ radians

# 13.
## Brief Explanations:
The area of a sector is $A=\frac{1}{2}r^{2}\theta$. Given $r = 12$ cm and $\theta=\frac{\pi}{6}$ radians. Then $A=\frac{1}{2}\times12^{2}\times\frac{\pi}{6}= 12\pi$ square cm.
# Answer:
b. $12\pi$ square cm

# 14.
## Brief Explanations:
A full circle has $2\pi$ radians. A quarter of a circle has $\frac{2\pi}{4}=\frac{\pi}{2}$ radians.
# Answer:
a. $\frac{\pi}{2}$ radians

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Explanation:

8.

Answer:

9.