SAT Math
Circles
Circles is a skill in the Geometry and Trigonometry domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.
13 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
A circle with center O has a circumference of 18π. Points A and B lie on the circle so that central angle AOB measures 80°. What is the length of minor arc AB?
- A. 8π
- B. 9π
- C. 14π
- D. 4π ✓
Correct answer: D. Arc length is the same fraction of the circumference as the central angle is of 360°: (80/360)(18π) = (2/9)(18π) = 4π.
A circle in the xy-plane is defined by the equation (x + 4)² + (y − 7)² = 121. What are the center and radius of the circle?
- A. Center (−4, 7), radius 11 ✓
- B. Center (−4, 7), radius 121
- C. Center (−4, −7), radius 11
- D. Center (4, −7), radius 11
Correct answer: A. In the standard form (x − h)² + (y − k)² = r², the center is (h, k) and the radius is √r²; here h = −4, k = 7, and r = √121 = 11.
What is the value of sin(17π/3)?
- A. −1/2
- B. −√3/2 ✓
- C. √3/2
- D. 1/2
Correct answer: B. Since 17π/3 − 4π = 5π/3, the angle is coterminal with 5π/3 (300°), which lies in the fourth quadrant with reference angle π/3; sine is negative there, so sin(17π/3) = −√3/2.
A circle has a circumference of 54. A central angle intercepts a minor arc, and that angle measures 40°. What is the length of the minor arc?
- A. 6 ✓
- B. 13.5
- C. 21.6
- D. 4.5
Correct answer: A. Correct — the arc length is the same fraction of the circumference as the central angle is of 360°: (40/360) × 54 = 6.
A circle in the xy-plane is defined by the equation x² + y² − 6x + 8y − 11 = 0. What is the radius of the circle?
- A. 11
- B. 6 ✓
- C. 36
- D. 4.24
Correct answer: B. Correct — completing the square gives (x − 3)² + (y + 4)² = 11 + 9 + 16 = 36, so the radius is √36 = 6.