Bluebook SAT Test Circles 8 — Questions and Answers
Question 1: A circle passes through points (0,0), (6,0), and (0,8). What is the radius of the circle?
- 5 (Correct answer)
- 10
- 7
- √(100)
Correct answer: 5
The hypotenuse of the right triangle formed is √(6²+8²)=10, which is the diameter, so r=5.
Question 2: The equation of a circle is x² + y² − 2x + 4y − 20 = 0. What is the area of this circle?
- 25π (Correct answer)
- 5π
- 20π
- 100π
Correct answer: 25π
(x−1)²+(y+2)²=20+1+4=25; r=5; area=25π.
Question 3: A circle has radius r. A sector with central angle 2π/5 is cut out. What fraction of the circle's area does the sector represent?
- 1/5 (Correct answer)
- 2/5
- 2π/5
- 1/10
Correct answer: 1/5
Fraction = θ/(2π) = (2π/5)/(2π) = 1/5.
Question 4: What is the length of the longest chord of a circle with area 36π?
- 12 (Correct answer)
- 6
- 18
- 36
Correct answer: 12
r=6; the longest chord is the diameter = 2r = 12.
Question 5: In a circle, a central angle intercepts an arc of 150°. What is the central angle in radians?
- 5π/6 (Correct answer)
- 5π/12
- 3π/5
- 7π/6
Correct answer: 5π/6
150° × π/180° = 150π/180 = 5π/6.
Question 6: Two circles are concentric (same center). The outer circle has radius 10 and the inner circle has radius 6. What is the area of the ring (annulus) between them?
- 64π (Correct answer)
- 100π
- 36π
- 16π
Correct answer: 64π
Area = π(10²) − π(6²) = 100π − 36π = 64π.
Question 7: A circle has equation (x−3)²+(y+2)²=50. The point (3+t, −2) lies on the circle. What is the positive value of t?
- 5√2 (Correct answer)
- 5
- √50
- 10
Correct answer: 5√2
(3+t−3)²+(−2+2)²=50 → t²=50 → t=√50=5√2.
Bluebook SAT Test Circles 8
A circle passes through points (0,0), (6,0), and (0,8).
What is the radius of the circle?