Bluebook SAT Test Circles 7 — Questions and Answers
Question 1: A circle has area 25π. What is the circumference?
- 10π (Correct answer)
- 5π
- 50π
- 25π
Correct answer: 10π
πr²=25π → r=5; circumference=2π(5)=10π.
Question 2: Convert 210° to radians.
- 7π/6 (Correct answer)
- 7π/4
- 3π/2
- 5π/6
Correct answer: 7π/6
210° × (π/180°) = 210π/180 = 7π/6.
Question 3: The circle x² + y² = 25 has center at the origin. Which of the following points lies inside the circle?
- (3, 3) (Correct answer)
- (5, 0)
- (4, 3)
- (0, 6)
Correct answer: (3, 3)
3²+3²=18<25, so (3,3) is inside; all others satisfy x²+y² ≥ 25.
Question 4: A sector has central angle 3π/2 radians and area 27π/2. What is the radius?
- 3 (Correct answer)
- 6
- 9
- √27
Correct answer: 3
A=½r²θ → 27π/2=½r²(3π/2)=(3πr²/4) → r²=9 → r=3.
Question 5: The central angle in a circle is 5 times the inscribed angle intercepting the same arc. What is the inscribed angle?
- This cannot happen; a central angle is always exactly 2× the inscribed angle (Correct answer)
- The inscribed angle is 36°
- The inscribed angle is 72°
- The inscribed angle is 45°
Correct answer: This cannot happen; a central angle is always exactly 2× the inscribed angle
By the Inscribed Angle Theorem, the central angle is always exactly twice the inscribed angle—it can never be 5 times it.
Question 6: A circle has center (−3, 2). Which equation could represent this circle?
- (x + 3)² + (y − 2)² = 10 (Correct answer)
- (x − 3)² + (y + 2)² = 10
- (x + 3)² + (y + 2)² = 10
- (x − 3)² + (y − 2)² = 10
Correct answer: (x + 3)² + (y − 2)² = 10
Center (−3, 2) gives (x−(−3))²+(y−2)²=r² → (x+3)²+(y−2)²=r².
Question 7: The length of an arc is 8π and the radius is 16. What is the central angle in degrees?
- 90° (Correct answer)
- 45°
- 180°
- 60°
Correct answer: 90°
Arc = (θ/360°)·2πr → 8π = (θ/360°)·32π → θ/360° = 1/4 → θ = 90°.
Bluebook SAT Test Circles 7
A circle has area 25π.
What is the circumference?