Bluebook SAT Test Circles 4 — Questions and Answers
Question 1: What is the center of the circle x² + y² − 10x + 4y + 20 = 0?
- (5, −2) (Correct answer)
- (−5, 2)
- (10, −4)
- (5, 2)
Correct answer: (5, −2)
Complete the square: (x−5)²+(y+2)² = 25+4−20 = 9; center (5,−2).
Question 2: A central angle of π/6 radians corresponds to how many degrees?
- 30° (Correct answer)
- 60°
- 45°
- 15°
Correct answer: 30°
(π/6)(180°/π) = 180°/6 = 30°.
Question 3: A circle has diameter 14. What is its area?
- 49π (Correct answer)
- 196π
- 14π
- 28π
Correct answer: 49π
r = 14/2 = 7; area = π(7)² = 49π.
Question 4: An arc subtends a central angle of 5π/6 radians in a circle of radius 6. What is the arc length?
- 5π (Correct answer)
- 10π
- 6π
- 3π
Correct answer: 5π
s = rθ = 6·(5π/6) = 5π.
Question 5: Two inscribed angles in the same circle intercept the same arc. What is the relationship between the two angles?
- They are equal (Correct answer)
- One is double the other
- They are supplementary
- They are complementary
Correct answer: They are equal
Inscribed angles that intercept the same arc are equal (both equal half the arc measure).
Question 6: A circle has area 64π. How long is an arc that subtends a central angle of 45°?
- 2π (Correct answer)
- 4π
- 8π
- π
Correct answer: 2π
r² = 64 → r = 8; arc = (45/360)(2π·8) = (1/8)(16π) = 2π.
Question 7: The circle (x + 4)² + (y − 1)² = 36 has been graphed. Which point lies on the circle?
- (2, 1)
- (−4, 7) (Correct answer)
- (0, 1)
- (4, 1)
Correct answer: (−4, 7)
For (−4, 7): (−4+4)² + (7−1)² = 0 + 36 = 36 ✓.
Bluebook SAT Test Circles 4
What is the center of the circle x² + y² − 10x + 4y + 20 = 0?