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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.

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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

How many points does a tangent line share with a circle?

Please select an answer first.

Correct answer: A

The correct answer is One point..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: A tangent touches a circle at exactly one point.
  3. Check the result: The correct answer is One point..

A tangent touches a circle at exactly one point.

2. QuestionMultiple choice

What is the relationship between a radius and tangent at the point of tangency?

Please select an answer first.

Correct answer: B

The correct answer is They are perpendicular..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The radius to the point of tangency forms a right angle with the tangent.
  3. Check the result: The correct answer is They are perpendicular..

The radius to the point of tangency forms a right angle with the tangent.

3. QuestionMultiple choice

Two tangent segments from the same external point are...

Please select an answer first.

Correct answer: C

The correct answer is Congruent..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Tangent segments drawn from a common external point have equal lengths.
  3. Check the result: The correct answer is Congruent..

Tangent segments drawn from a common external point have equal lengths.

4. QuestionMultiple choice

If two chords intersect inside a circle, what does the Chord-Chord Product Theorem state?

Please select an answer first.

Correct answer: D

The correct answer is The products of the two chord parts are equal..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: For intersecting chords, the product of the parts of one chord equals the product of the parts of the other.
  3. Check the result: The correct answer is The products of the two chord parts are equal..

For intersecting chords, the product of the parts of one chord equals the product of the parts of the other.

5. QuestionMultiple choice

Two chords have parts 3 and 4, and 2 and x. What is x?

Please select an answer first.

Correct answer: A

The correct answer is 6..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Use 3 · 4 = 2x, so x = 6.
  3. Check the result: The correct answer is 6..

Use 3 · 4 = 2x, so x = 6.

6. QuestionMultiple choice

A tangent has length 6 and a secant has external part 4. What is the secant’s whole length?

Please select an answer first.

Correct answer: B

The correct answer is 9..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: By the tangent-secant theorem, \6^2=4x\, so x = 9.
  3. Check the result: The correct answer is 9..

By the tangent-secant theorem, \6^2=4x\, so x = 9.

7. QuestionMultiple choice

Two secants have external and whole lengths 3 and 12, and 4 and x. What is x?

Please select an answer first.

Correct answer: C

The correct answer is 9..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: Use 3 · 12 = 4x, so 36 = 4x and x = 9.
  3. Check the result: The correct answer is 9..

Use 3 · 12 = 4x, so 36 = 4x and x = 9.

8. QuestionMultiple choice

A chord is perpendicular to a radius from the center. What does the radius do to the chord?

Please select an answer first.

Correct answer: D

The correct answer is It bisects the chord..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: A radius or diameter perpendicular to a chord bisects the chord.
  3. Check the result: The correct answer is It bisects the chord..

A radius or diameter perpendicular to a chord bisects the chord.

9. QuestionMultiple choice

A circle has radius 10 and a chord is 6 units from the center. What is half the chord length?

Please select an answer first.

Correct answer: A

The correct answer is 8 units..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The radius, half-chord, and center-to-chord distance form a right triangle: \x=\\sqrt{10^2-6^2}=8\.
  3. Check the result: The correct answer is 8 units..

The radius, half-chord, and center-to-chord distance form a right triangle: \x=\\sqrt{10^2-6^2}=8\.

10. QuestionMultiple choice

If PA is tangent to a circle at A and O is the center, what is true?

Please select an answer first.

Correct answer: B

The correct answer is OA is perpendicular to PA..

  1. Identify the circle information: Mark the center, radius, diameter, chord, arc, angle, tangent, or coordinate information given.
  2. Apply the circle relationship: The radius OA is perpendicular to tangent PA at the point of tangency.
  3. Check the result: The correct answer is OA is perpendicular to PA..

The radius OA is perpendicular to tangent PA at the point of tangency.

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