Question
Question 1.
A circle has a center point upper C. Points upper D, upper E, upper F and upper G lie on the circumference of the circle.
If CH=42 m and CF=58 m, then what is the length of FG?
(1 point)
Responses
16 m
16 m
32 m
32 m
80 m
80 m
40 m
40 m
Question 2
Question 2.
A circle has center point upper O. Upper O connects to a point on the circumference labeled upper B. Upper B connects to a point outside the circle labeled upper A. A diagonal line connects upper A and upper O to form the shape of a triangle.
If BO=45 in. and BA=108 in., then what is the length of AO to the nearest whole inch?
(1 point)
Responses
25 in
25 in
117 in
117 in
98 in
98 in
67 in
67 in
Question 3
Question 3.
A circle has a center point marked as upper G. Points upper H, upper I, upper J and upper K lie on the circumference of the circle.
If arc KJ=13x−10 and arc JI=7x−10, then find the m∠KIJ.
(1 point)
Responses
120°
120°
80°
80°
60°
60°
10°
10°
Question 4
Question 4.
Triangle XYZ is inscribed inside a circle with diameter XZ and the inscribed angle at Y. The angle measure at X is 59°. Using what you know about inscribed angles, find the arc measure of XY.
(1 point)
Responses
31°
31°
118°
118°
62°
62°
298°
298°
Question 5
Question 5.
Quadrilateral upper A upper B upper C upper D is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of <A.
(1 point)
Responses
53°
53°
106°
106°
98°
98°
82°
82°
Question 6
Question 6.
Quadrilateral upper A upper B upper C upper D is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of <C.
(1 point)
Responses
58°
58°
87°
87°
98°
98°
80°
80°
Question 7
Question 7.
Quadrilateral upper A upper B upper C upper D is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of <D.
(1 point)
Responses
82°
82°
98°
98°
116°
116°
87°
87°
Question 8
Question 8.
Jamila wants to walk with her friend at the park but isn’t sure how long the course is. She knows it is a circular path with a walkway through the middle, and the path across the middle is 12
of a mile. What is the distance all the way around the circle? Give the answer to the nearest tenth of a mile.
(1 point)
Responses
1.6 mi
1.6 mi
3.1 mi
3.1 mi
18.8 mi
18.8 mi
0.8 mi
0.8 mi
Question 9
Question 9.
If the area of a circle is 586 m², then what is the length of the diameter to the nearest meter? ( A = π * r² )
(1 point)
Responses
293 m
293 m
27 m
27 m
187 m
187 m
12 m
12 m
Question 10
Question 10.
If a circle has a central angle of 125° and a radius of 27 millimeters, how long is the arc formed by that angle? Leave your answer in terms of π.
(1 point)
Responses
2025π8 mm
2025π8 mm
75π4 mm
75π4 mm
75π8 mm
75π8 mm
54π mm
54π mm
Question 11
Question 11.
What is the area of the sector of a circle with a central angle of 216° and a radius of 7 inches? Leave your answer rounded to the nearest tenth.
(1 point)
Responses
26.4 inches
26.4 inches
92.4 inches
92.4 inches
13.2 inches
13.2 inches
29.4 inches
29.4 inches
Question 12
Question 12.
A cookie cake has a diameter of 18 in. If part of the cookie cake is eaten, the missing section forms an angle of 270°. What is the area of the cookie cake that was eaten? Round your answer to the nearest tenth.
(1 point)
Responses
190.9 in²
190.9 in²
254.5 in²
254.5 in²
127.2 in²
127.2 in²
63.6 in²
A circle has a center point upper C. Points upper D, upper E, upper F and upper G lie on the circumference of the circle.
If CH=42 m and CF=58 m, then what is the length of FG?
(1 point)
Responses
16 m
16 m
32 m
32 m
80 m
80 m
40 m
40 m
Question 2
Question 2.
A circle has center point upper O. Upper O connects to a point on the circumference labeled upper B. Upper B connects to a point outside the circle labeled upper A. A diagonal line connects upper A and upper O to form the shape of a triangle.
If BO=45 in. and BA=108 in., then what is the length of AO to the nearest whole inch?
(1 point)
Responses
25 in
25 in
117 in
117 in
98 in
98 in
67 in
67 in
Question 3
Question 3.
A circle has a center point marked as upper G. Points upper H, upper I, upper J and upper K lie on the circumference of the circle.
If arc KJ=13x−10 and arc JI=7x−10, then find the m∠KIJ.
(1 point)
Responses
120°
120°
80°
80°
60°
60°
10°
10°
Question 4
Question 4.
Triangle XYZ is inscribed inside a circle with diameter XZ and the inscribed angle at Y. The angle measure at X is 59°. Using what you know about inscribed angles, find the arc measure of XY.
(1 point)
Responses
31°
31°
118°
118°
62°
62°
298°
298°
Question 5
Question 5.
Quadrilateral upper A upper B upper C upper D is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of <A.
(1 point)
Responses
53°
53°
106°
106°
98°
98°
82°
82°
Question 6
Question 6.
Quadrilateral upper A upper B upper C upper D is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of <C.
(1 point)
Responses
58°
58°
87°
87°
98°
98°
80°
80°
Question 7
Question 7.
Quadrilateral upper A upper B upper C upper D is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of <D.
(1 point)
Responses
82°
82°
98°
98°
116°
116°
87°
87°
Question 8
Question 8.
Jamila wants to walk with her friend at the park but isn’t sure how long the course is. She knows it is a circular path with a walkway through the middle, and the path across the middle is 12
of a mile. What is the distance all the way around the circle? Give the answer to the nearest tenth of a mile.
(1 point)
Responses
1.6 mi
1.6 mi
3.1 mi
3.1 mi
18.8 mi
18.8 mi
0.8 mi
0.8 mi
Question 9
Question 9.
If the area of a circle is 586 m², then what is the length of the diameter to the nearest meter? ( A = π * r² )
(1 point)
Responses
293 m
293 m
27 m
27 m
187 m
187 m
12 m
12 m
Question 10
Question 10.
If a circle has a central angle of 125° and a radius of 27 millimeters, how long is the arc formed by that angle? Leave your answer in terms of π.
(1 point)
Responses
2025π8 mm
2025π8 mm
75π4 mm
75π4 mm
75π8 mm
75π8 mm
54π mm
54π mm
Question 11
Question 11.
What is the area of the sector of a circle with a central angle of 216° and a radius of 7 inches? Leave your answer rounded to the nearest tenth.
(1 point)
Responses
26.4 inches
26.4 inches
92.4 inches
92.4 inches
13.2 inches
13.2 inches
29.4 inches
29.4 inches
Question 12
Question 12.
A cookie cake has a diameter of 18 in. If part of the cookie cake is eaten, the missing section forms an angle of 270°. What is the area of the cookie cake that was eaten? Round your answer to the nearest tenth.
(1 point)
Responses
190.9 in²
190.9 in²
254.5 in²
254.5 in²
127.2 in²
127.2 in²
63.6 in²
Answers
GPT-4o mini
Here are the answers to the questions provided:
**Question 1:** A circle has a center point C. Points D, E, F, and G lie on the circumference of the circle.
If CH = 42 m and CF = 58 m, then what is the length of FG?
**Answer:** 16 m
---
**Question 2:** A circle has center point O. O connects to a point on the circumference labeled B. B connects to a point outside the circle labeled A.
If BO = 45 in. and BA = 108 in., then what is the length of AO to the nearest whole inch?
**Answer:** 98 in
---
**Question 3:** A circle has a center point marked as G. Points H, I, J, and K lie on the circumference of the circle.
If arc KJ = 13x - 10 and arc JI = 7x - 10, then find the m∠KIJ.
Assuming that m∠KIJ = (arc KJ + arc JI)/2, we find:
**Answer:** 80°
---
**Question 4:** Triangle XYZ is inscribed inside a circle with diameter XZ and the inscribed angle at Y. The angle measure at X is 59°.
Using what you know about inscribed angles, find the arc measure of XY.
The arc measure of XY will be double the angle at Y.
**Answer:** 118°
---
**Question 5:** Quadrilateral ABCD is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of ∠A.
Using opposite angles in a cyclic quadrilateral: ∠A + ∠C + 93° + (1/2)(106°) = 180°
**Answer:** 106°
---
**Question 6:** Same conditions as Question 5. Find the measure of ∠C.
Using opposite angles in cyclic quadrilateral: ∠A + ∠C + 93° + (1/2)(58°) = 180°
**Answer:** 98°
---
**Question 7:** Same conditions as Question 5. Find the measure of ∠D.
Using angles in a cyclic quadrilateral: ∠D + 93° + (1/2)(106°) + (1/2)(58°) = 180°
**Answer:** 87°
---
**Question 8:** Jamila wants to know the length of the circular path with a walkway across it being 12 miles.
The diameter is 12 miles, therefore the circumference is C = πd.
**Answer:** 37.7 mi (which rounds up to 3.1 mi for the closest tenth of a mile)
---
**Question 9:** If the area of a circle is 586 m², then what is the length of the diameter to the nearest meter?
A = πr² → 586 = πr² → r² = 586/π → r = √(586/π) → d = 2r.
**Answer:** 27 m
---
**Question 10:** If a circle has a central angle of 125° and a radius of 27 millimeters, how long is the arc formed by that angle?
Arc Length Formula: L = (θ/360°) * 2πr.
**Answer:** 75π/4 mm
---
**Question 11:** What is the area of the sector of a circle with a central angle of 216° and a radius of 7 inches?
Area of a Sector Formula: A = (θ/360°) * πr².
**Answer:** 26.4 inches
---
**Question 12:** A cookie cake has a diameter of 18 in. If part of the cookie cake is eaten, the missing section forms an angle of 270°.
Area of Circle: A = πr²; Area eaten = (270/360) * Area of Cake.
**Answer:** 127.2 in²
---
These answers sum up various properties of circles, angles, and sectors based on the inputs provided for each question.
**Question 1:** A circle has a center point C. Points D, E, F, and G lie on the circumference of the circle.
If CH = 42 m and CF = 58 m, then what is the length of FG?
**Answer:** 16 m
---
**Question 2:** A circle has center point O. O connects to a point on the circumference labeled B. B connects to a point outside the circle labeled A.
If BO = 45 in. and BA = 108 in., then what is the length of AO to the nearest whole inch?
**Answer:** 98 in
---
**Question 3:** A circle has a center point marked as G. Points H, I, J, and K lie on the circumference of the circle.
If arc KJ = 13x - 10 and arc JI = 7x - 10, then find the m∠KIJ.
Assuming that m∠KIJ = (arc KJ + arc JI)/2, we find:
**Answer:** 80°
---
**Question 4:** Triangle XYZ is inscribed inside a circle with diameter XZ and the inscribed angle at Y. The angle measure at X is 59°.
Using what you know about inscribed angles, find the arc measure of XY.
The arc measure of XY will be double the angle at Y.
**Answer:** 118°
---
**Question 5:** Quadrilateral ABCD is drawn within a circle such that all vertices touch the edge of the circle.
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of ∠A.
Using opposite angles in a cyclic quadrilateral: ∠A + ∠C + 93° + (1/2)(106°) = 180°
**Answer:** 106°
---
**Question 6:** Same conditions as Question 5. Find the measure of ∠C.
Using opposite angles in cyclic quadrilateral: ∠A + ∠C + 93° + (1/2)(58°) = 180°
**Answer:** 98°
---
**Question 7:** Same conditions as Question 5. Find the measure of ∠D.
Using angles in a cyclic quadrilateral: ∠D + 93° + (1/2)(106°) + (1/2)(58°) = 180°
**Answer:** 87°
---
**Question 8:** Jamila wants to know the length of the circular path with a walkway across it being 12 miles.
The diameter is 12 miles, therefore the circumference is C = πd.
**Answer:** 37.7 mi (which rounds up to 3.1 mi for the closest tenth of a mile)
---
**Question 9:** If the area of a circle is 586 m², then what is the length of the diameter to the nearest meter?
A = πr² → 586 = πr² → r² = 586/π → r = √(586/π) → d = 2r.
**Answer:** 27 m
---
**Question 10:** If a circle has a central angle of 125° and a radius of 27 millimeters, how long is the arc formed by that angle?
Arc Length Formula: L = (θ/360°) * 2πr.
**Answer:** 75π/4 mm
---
**Question 11:** What is the area of the sector of a circle with a central angle of 216° and a radius of 7 inches?
Area of a Sector Formula: A = (θ/360°) * πr².
**Answer:** 26.4 inches
---
**Question 12:** A cookie cake has a diameter of 18 in. If part of the cookie cake is eaten, the missing section forms an angle of 270°.
Area of Circle: A = πr²; Area eaten = (270/360) * Area of Cake.
**Answer:** 127.2 in²
---
These answers sum up various properties of circles, angles, and sectors based on the inputs provided for each question.