Circles Practice Questions
Common Core (US) · Common Core Geometry · 144 free MCQs with instant results and detailed explanations.
144
Total
43
Easy
84
Medium
17
Hard
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Sample Questions from Circles
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
Two circles have the same center but different radii. What are these circles called?
A.
Concentric circles
B.
Tangent circles
C.
Intersecting circles
D.
Secant circles
Show Answer & Explanation
Correct Answer: A
Circles that share the same center but have different radii are called concentric circles. This means they are nested within each other without touching.
Q2
Easy
If a circle has a diameter of 10 inches, what is its radius?
A.
5 inches
B.
10 inches
C.
20 inches
D.
15 inches
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Correct Answer: A
The radius of a circle is half of its diameter. Given that the diameter is 10 inches, the radius is 10/2 = 5 inches.
Q3
Easy
A circle has a radius of 4 inches. If a chord is 6 inches long, what is the distance from the center of the circle to the chord?
A.
2 inches
B.
3 inches
C.
4 inches
D.
5 inches
Show Answer & Explanation
Correct Answer: B
Using the properties of circles, the distance from the center to the chord can be found using the formula h = โ(rยฒ - (c/2)ยฒ) where r is the radius and c is the chord length. Here, h = โ(4ยฒ - (6/2)ยฒ) = โ(16 - 9) = โ7, approximately 3 inches.
Q4
Medium
What is the circumference of a circle with a radius of 7 cm? (Use ฯ โ 3.14)
A.
43.96 cm
B.
21.98 cm
C.
14.00 cm
D.
31.42 cm
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Correct Answer: A
The circumference of a circle is calculated as C = 2ฯr. Substituting the radius (7 cm) gives C = 2 ร 3.14 ร 7 = 43.96 cm.
Q5
Medium
If the diameter of a circular park is 20 meters, what is the area of the park? (Use ฯ โ 3.14)
A.
314 mยฒ
B.
78.5 mยฒ
C.
100 mยฒ
D.
157 mยฒ
Show Answer & Explanation
Correct Answer: A
Area of a circle is A = ฯrยฒ. The radius (r) is half the diameter, so r = 10 m. Thus, A = 3.14 ร (10)ยฒ = 314 mยฒ.
Q6
Medium
What is the angle subtended at the center of a circle by an arc length of 10 cm if the radius of the circle is 5 cm?
A.
72 degrees
B.
60 degrees
C.
90 degrees
D.
36 degrees
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Correct Answer: A
The formula for the angle in radians is ฮธ = arc length / radius. Converting to degrees: ฮธ = (10 / 5) ร (180/ฯ), which gives approximately 72 degrees.
Q7
Medium
If the diameter of a circle is doubled, how does the area change?
A.
Increases by a factor of 2
B.
Increases by a factor of 4
C.
Remains the same
D.
Increases by a factor of 3
Show Answer & Explanation
Correct Answer: B
The area A of a circle is given by A = ฯrยฒ. If the diameter is doubled, the radius also doubles (r becomes 2r), leading to an area of A = ฯ(2r)ยฒ = 4ฯrยฒ, which is 4 times the original area.
Q8
Hard
A circle has a radius of 10 cm. A chord of the circle is 12 cm long. What is the distance from the center of the circle to the chord?
A.
8 cm
B.
6 cm
C.
5 cm
D.
10 cm
Show Answer & Explanation
Correct Answer: B
The distance from the center to the chord can be found using the formula d = sqrt(r^2 - (c/2)^2), where r is the radius and c is the length of the chord. Plugging in the values, we get d = sqrt(10^2 - (12/2)^2) = sqrt(100 - 36) = sqrt(64) = 8. However, the distance from the center to the chord is 10 - 8 = 6 cm.
Q9
Hard
Two tangent lines are drawn from a point outside a circle to the circle. If the lengths of the tangent segments are both 10 cm, what is the distance from the external point to the center of the circle?
A.
10โ2 cm
B.
20 cm
C.
15 cm
D.
10 cm
Show Answer & Explanation
Correct Answer: A
When two tangents are drawn from a point outside a circle, they are equal in length. The distance from the point to the center of the circle is the hypotenuse of a right triangle formed, where each tangent segment is one leg (10 cm). Using the Pythagorean theorem: dยฒ = 10ยฒ + rยฒ, where r is the radius (which is also 10 cm here, making d = 10โ2 cm). Therefore, option A is correct.
Q10
Hard
A sector of a circle has a central angle of 60 degrees and a radius of 5 inches. What is the area of the sector?
A.
13.09 inยฒ
B.
10.42 inยฒ
C.
5.24 inยฒ
D.
15.70 inยฒ
Show Answer & Explanation
Correct Answer: A
The area of a sector can be calculated using the formula: Area = (ฮธ/360) * ฯ * rยฒ, where ฮธ is the central angle in degrees and r is the radius. Substituting the values: Area = (60/360) * ฯ * 5ยฒ = (1/6) * ฯ * 25 = (25ฯ/6) โ 13.09 inยฒ.
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Practice All 144 Questions →Circles โ Common Core (US) Common Core Geometry Practice Questions Online
This page contains 144 practice MCQs for the chapter Circles in Common Core (US) Common Core Geometry. The questions are organized by difficulty โ 43 easy, 84 medium, 17 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.