NumicornNumicornLearn, solve, progress

Circles Practice Tests

These Grade 10 Geometry practice tests develop circle vocabulary, measurement formulas, arc and angle reasoning, chord and tangent theorems, sectors, and coordinate applications.

Skills covered

  • Identifying centers, radii, diameters, chords, secants, tangents, arcs, sectors, and central angles
  • Using circumference, area, arc length, sector area, radius, and diameter formulas
  • Applying central-angle, inscribed-angle, semicircle, tangent-radius, and chord theorems
  • Using chord-chord, tangent-secant, and secant-secant product relationships
  • Writing circle equations and solving coordinate, rotation, tire, map, and real-world measurement problems

How to use these practice tests

Start by identifying the circle part or theorem involved. Then decide whether the problem uses radius or diameter and whether an arc or sector is a fraction of the full circle.

For more Grade 10 Math practice, return to the Grade 10 Math category.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

5. Test

Grade 10 Circles Practice Tests

Practice Grade 10 Geometry questions about circle vocabulary, circumference, area, arcs, angles, chords, tangents, secants, sectors, and coordinate equations.

Choose the best answer. Identify the circle element or theorem, use the appropriate formula, and keep angle measures, radius, diameter, and units consistent.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the standard equation of a circle centered at (h,k) with radius r?

Please select an answer first.

Correct answer: A

The correct answer is (x−h)2+(y−k)2=r2(x-h)^2+(y-k)^2=r^2..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The standard circle equation uses squared horizontal and vertical distances from the center.
  3. Check the result: The correct answer is (x−h)2+(y−k)2=r2(x-h)^2+(y-k)^2=r^2..

The standard circle equation uses squared horizontal and vertical distances from the center.

2. QuestionMultiple choice

What is the equation of a circle with center (2, −3) and radius 4?

Please select an answer first.

Correct answer: B

The correct answer is (x−2)2+(y+3)2=16(x-2)^2+(y+3)^2=16..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Substitute h = 2, k = −3, and r = 4 into the standard equation.
  3. Check the result: The correct answer is (x−2)2+(y+3)2=16(x-2)^2+(y+3)^2=16..

Substitute h = 2, k = −3, and r = 4 into the standard equation.

3. QuestionMultiple choice

Which point lies on the circle x2+y2=25x^2+y^2=25?

Please select an answer first.

Correct answer: C

The correct answer is (3, 4)..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: For (3,4), 32+42=9+16=253^2+4^2=9+16=25, so the point lies on the circle.
  3. Check the result: The correct answer is (3, 4)..

For (3,4), 32+42=9+16=253^2+4^2=9+16=25, so the point lies on the circle.

4. QuestionMultiple choice

What is the center of a circle whose diameter endpoints are (−2, 4) and (6, 10)?

Please select an answer first.

Correct answer: D

The correct answer is (2, 7)..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The center is the midpoint: ((−2 + 6)/2, (4 + 10)/2) = (2,7).
  3. Check the result: The correct answer is (2, 7)..

The center is the midpoint: ((−2 + 6)/2, (4 + 10)/2) = (2,7).

5. QuestionMultiple choice

What is the radius of a circle centered at (0,0) through point (6,8)?

Please select an answer first.

Correct answer: A

The correct answer is 10..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Use the distance formula: r=62+82=10r=\sqrt{6^2+8^2}=10.
  3. Check the result: The correct answer is 10..

Use the distance formula: r=62+82=10r=\sqrt{6^2+8^2}=10.

6. QuestionMultiple choice

What is the arc length of a 90° sector with radius 8?

Please select an answer first.

Correct answer: B

The correct answer is 4π4\pi..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: A 90-degree arc is one-fourth of the circumference 2π(8)2\pi(8), so its length is 4π4\pi.
  3. Check the result: The correct answer is 4π4\pi..

A 90-degree arc is one-fourth of the circumference 2π(8)2\pi(8), so its length is 4π4\pi.

7. QuestionMultiple choice

What is the area of a 60° sector with radius 6?

Please select an answer first.

Correct answer: C

The correct answer is 6π6\pi square units..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: A 60-degree sector is one-sixth of π(6)2=36π\pi(6)^2=36\pi, giving 6π6\pi.
  3. Check the result: The correct answer is 6π6\pi square units..

A 60-degree sector is one-sixth of π(6)2=36π\pi(6)^2=36\pi, giving 6π6\pi.

8. QuestionMultiple choice

A tire has circumference 2 m. How far does it travel in 15 complete rotations?

Please select an answer first.

Correct answer: D

The correct answer is 30 m..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Distance equals circumference times rotations: 2 · 15 = 30 meters.
  3. Check the result: The correct answer is 30 m..

Distance equals circumference times rotations: 2 · 15 = 30 meters.

9. QuestionMultiple choice

A circular garden has radius 7 m. What is its perimeter?

Please select an answer first.

Correct answer: A

The correct answer is 14π14\pi m..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Perimeter is circumference: C=2π(7)=14πC=2\pi(7)=14\pi meters.
  3. Check the result: The correct answer is 14π14\pi m..

Perimeter is circumference: C=2π(7)=14πC=2\pi(7)=14\pi meters.

10. QuestionMultiple choice

Which expression gives the area of a sector with central angle θ degrees and radius r?

Please select an answer first.

Correct answer: B

The correct answer is θ360πr2\frac{\theta}{360}\pi r^2..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: A sector is the fraction θ/360 of the full circle area πr2\pi r^2.
  3. Check the result: The correct answer is θ360πr2\frac{\theta}{360}\pi r^2..

A sector is the fraction θ/360 of the full circle area πr2\pi r^2.

Previous testNext test