Bluebook SAT Test Circles 10 — Questions and Answers
Question 1: A circle passes through the origin. Its center is at (5, 0). What is the equation of the circle?
- x² + y² = 25
- (x−5)² + y² = 25 (Correct answer)
- x² + y² = 5
- (x+5)² + y² = 25
Correct answer: (x−5)² + y² = 25
The radius = distance from (5,0) to (0,0) = 5. Equation: (x−5)² + y² = 25.
Question 2: In a circle, an inscribed angle measures 47°. Another inscribed angle intercepts the same arc. What is its measure?
- 94°
- 47° (Correct answer)
- 133°
- 23.5°
Correct answer: 47°
Inscribed angles that intercept the same arc are equal in measure.
Question 3: A circle has circumference C. What is the area of the circle in terms of C?
- C²/π
- C²/(2π)
- C²/(4π) (Correct answer)
- πC²
Correct answer: C²/(4π)
C = 2πr so r = C/(2π). Area = πr² = π(C/(2π))² = πC²/(4π²) = C²/(4π).
Question 4: The circle (x−2)² + (y+3)² = r² passes through the point (−1, 1). What is r²?
- 9
- 13
- 25 (Correct answer)
- 18
Correct answer: 25
r² = (−1−2)² + (1−(−3))² = (−3)² + 4² = 9 + 16 = 25.
Question 5: Two circles have radii in the ratio 2:5. The area of the smaller circle is 12π. What is the area of the larger circle?
- 30π
- 75π (Correct answer)
- 50π
- 60π
Correct answer: 75π
Area ratio = (2:5)² = 4:25. If smaller area = 12π, larger = 12π × (25/4) = 75π.
Question 6: A sector has a central angle of 3π/4 radians and arc length 9π/2. What is the radius?
- 4
- 6 (Correct answer)
- 3
- 12
Correct answer: 6
Arc length = rθ, so 9π/2 = r × (3π/4). r = (9π/2) ÷ (3π/4) = (9π/2) × (4/(3π)) = 6.
Question 7: A circle has center O and radius 10. Chord AB has length 16. What is the distance from O to the midpoint of AB?
- 6
- 8
- √(100−64)
- Both A and C (Correct answer)
Correct answer: Both A and C
The perpendicular from O to chord AB meets AB at its midpoint, and the distance = √(10² − 8²) = √(100−64) = √36 = 6. Both answer A (6) and answer C (√36 = 6) are correct.
Bluebook SAT Test Circles 10
A circle passes through the origin.
Its center is at (5, 0).
What is the equation of the circle?