SAT Circles

Circle questions test the equation of a circle in the coordinate plane, plus arcs, sectors and central angles. In the equation, the centre coordinates appear with opposite signs and the number on the right is the radius squared — both are routinely misread.

Practise this skill freeHow the SAT is structured
MathGeometry and Trigonometry67 questions
The trap on this skill

Reversing the signs of the center coordinates or using r instead of r squared.

How this skill behaves

What 67 questions on it look like

90% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

Not one question in this skill is rated hard. What makes it cost marks is speed and carelessness, not difficulty.

medium90%
easy10%

Difficulty mix across the 67 questions in this skill.

From the bank

Three real circles questions

Each one explains the credited answer and why every other option fails.

Geometry and Trigonometry · medium

A circular boundary on the pool side meter wrapping diagram is represented in the xy-plane with center (6, -4) and radius 5. Which equation represents the circle?

  1. A(x + 6)^2 + (y - 4)^2 = 25
  2. B(x - 6)^2 + (y + 4)^2 = 5
  3. C(x + 6)^2 + (y - 4)^2 = 5
  4. D(x - 6)^2 + (y + 4)^2 = 25correct
Why D is correct — and why the others are not

A circle with center (h, k) and radius r has equation (x - h)^2 + (y - k)^2 = r^2. Here that is (x - 6)^2 + (y + 4)^2 = 25. This matches the evidence or condition involving Circles. A final check is using the relevant formula only after identifying its inputs.

A. This value results from reversing the signs of the center coordinates or using r instead of r squared

B. This value results from reversing the signs of the center coordinates or using r instead of r squared

C. This value results from reversing the signs of the center coordinates or using r instead of r squared

Geometry and Trigonometry · easy

A circular boundary on the workshop backup lamp stacking usage chart is represented in the xy-plane with center (2, -2) and radius 3. Which equation represents the circle?

  1. A(x + 2)^2 + (y - 2)^2 = 9
  2. B(x - 2)^2 + (y + 2)^2 = 9correct
  3. C(x - 2)^2 + (y + 2)^2 = 3
  4. D(x + 2)^2 + (y - 2)^2 = 3
Why B is correct — and why the others are not

A circle with center (h, k) and radius r has equation (x - h)^2 + (y - k)^2 = r^2. Here that is (x - 2)^2 + (y + 2)^2 = 9. The key support is the way the item treats Circles. A final check is tracking whether the prompt asks for a value or an expression.

A. This value results from reversing the signs of the center coordinates or using r instead of r squared

C. This value results from reversing the signs of the center coordinates or using r instead of r squared

D. This value results from reversing the signs of the center coordinates or using r instead of r squared

Geometry and Trigonometry · medium

A circular boundary on the rooftop exit wheel plotting layout note is represented in the xy-plane with center (2, -3) and radius 4. Which equation represents the circle?

  1. A(x + 2)^2 + (y - 3)^2 = 16
  2. B(x - 2)^2 + (y + 3)^2 = 16correct
  3. C(x - 2)^2 + (y + 3)^2 = 4
  4. D(x + 2)^2 + (y - 3)^2 = 4
Why B is correct — and why the others are not

A circle with center (h, k) and radius r has equation (x - h)^2 + (y - k)^2 = r^2. Here that is (x - 2)^2 + (y + 3)^2 = 16. The key support is the way the item treats Circles. A final check is keeping the denominator or scale attached to the result.

A. This value results from reversing the signs of the center coordinates or using r instead of r squared

C. This value results from reversing the signs of the center coordinates or using r instead of r squared

D. This value results from reversing the signs of the center coordinates or using r instead of r squared

67 questions on this skill, free to start.

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FAQ

Circles questions

What is the equation of a circle?

(x − h)² + (y − k)² = r², with centre (h, k) and radius r. A circle centred at (3, −2) shows as (x − 3)² + (y + 2)².

How do I find an arc length or sector area?

Take the fraction of the full circle the central angle represents, then apply it to the circumference or the area.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Right Triangle Trigonometry68 questionsLines, Angles, and Triangles67 questionsCoordinate Geometry60 questionsArea and Volume42 questions

Practise circles until the trap stops working.

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