Bluebook SAT Test Circles 1 — Questions and Answers
Question 1: What is the radius of the circle with equation x² + y² = 49?
- 7 (Correct answer)
- 49
- √49/2
- 24.5
Correct answer: 7
The standard form x² + y² = r² gives r² = 49, so r = 7.
Question 2: The center of the circle (x − 3)² + (y + 5)² = 16 is:
- (3, −5) (Correct answer)
- (−3, 5)
- (3, 5)
- (−3, −5)
Correct answer: (3, −5)
In (x − h)² + (y − k)² = r², the center is (h, k) = (3, −5).
Question 3: A circle has center (0, 0) and radius 5. What is the circumference?
- 10Ï€ (Correct answer)
- 25Ï€
- 5Ï€
- 2Ï€
Correct answer: 10Ï€
Circumference = 2Ï€r = 2Ï€(5) = 10Ï€.
Question 4: A circle has radius 6. What is its area?
- 36Ï€ (Correct answer)
- 12Ï€
- 6Ï€
- 72Ï€
Correct answer: 36Ï€
Area = πr² = π(6)² = 36π.
Question 5: An arc of a circle with radius 10 subtends a central angle of 90°. What is the arc length?
- 5Ï€ (Correct answer)
- 10Ï€
- 25Ï€
- 2.5Ï€
Correct answer: 5Ï€
Arc length = (θ/360°)·2πr = (90/360)·2π(10) = (1/4)(20π) = 5π.
Question 6: A central angle of a circle measures 120° and the radius is 9. What is the area of the corresponding sector?
- 27Ï€ (Correct answer)
- 54Ï€
- 18Ï€
- 81Ï€
Correct answer: 27Ï€
Sector area = (θ/360°)·πr² = (120/360)·π(81) = (1/3)(81π) = 27π.
Question 7: An inscribed angle in a circle measures 35°. What is the central angle that subtends the same arc?
- 70° (Correct answer)
- 35°
- 17.5°
- 140°
Correct answer: 70°
The Inscribed Angle Theorem states the central angle is twice the inscribed angle: 2 × 35° = 70°.
Bluebook SAT Test Circles 1
What is the radius of the circle with equation x² + y² = 49?