Bluebook SAT Test Circles 2 — Questions and Answers
Question 1: Which equation represents a circle with center (−2, 4) and radius 3?
- (x + 2)² + (y − 4)² = 9 (Correct answer)
- (x − 2)² + (y + 4)² = 9
- (x + 2)² + (y − 4)² = 3
- (x − 2)² + (y − 4)² = 9
Correct answer: (x + 2)² + (y − 4)² = 9
Center (−2, 4) and r = 3: (x − (−2))² + (y − 4)² = 3² gives (x + 2)² + (y − 4)² = 9.
Question 2: Convert the central angle 3π/4 radians to degrees.
- 135° (Correct answer)
- 270°
- 60°
- 45°
Correct answer: 135°
(3π/4) × (180°/π) = 3 × 45° = 135°.
Question 3: A circle has circumference 18π. What is its radius?
- 9 (Correct answer)
- 18
- 6
- 3
Correct answer: 9
C = 2πr → 18π = 2πr → r = 9.
Question 4: Two radii of a circle form a central angle of 60°. The radius is 12. What is the length of the arc between them?
- 4π (Correct answer)
- 12π
- 2π
- 6π
Correct answer: 4π
Arc = (60/360)(2π·12) = (1/6)(24π) = 4π.
Question 5: The equation x² + y² + 6x − 2y + 6 = 0 can be rewritten in standard form. What is the radius?
- 2 (Correct answer)
- 4
- 6
- √6
Correct answer: 2
Complete the square: (x²+6x+9)+(y²−2y+1) = −6+9+1 = 4; so (x+3)²+(y−1)²=4, radius = 2.
Question 6: A chord in a circle has a length equal to the radius. What is the central angle subtended by this chord?
- 60° (Correct answer)
- 90°
- 120°
- 45°
Correct answer: 60°
When chord length = radius, the triangle formed by the two radii and the chord is equilateral, giving a central angle of 60°.
Question 7: A sector of a circle has radius 8 and area 16π. What is the central angle in degrees?
- 90° (Correct answer)
- 45°
- 180°
- 120°
Correct answer: 90°
16π = (θ/360°)·π(64) → θ/360° = 16π/64π = 1/4 → θ = 90°.
Bluebook SAT Test Circles 2
Which equation represents a circle with center (−2, 4) and radius 3?