Bluebook SAT Test Circles 9 — Questions and Answers
Question 1: The equation of a circle is (x − 4)² + (y − 4)² = 16. Which of the following points lies on the circle?
- (4, 8)
- (8, 4)
- (0, 4)
- Both A and B (Correct answer)
Correct answer: Both A and B
(4−4)² + (8−4)² = 0 + 16 = 16 ✓; (8−4)² + (4−4)² = 16 + 0 = 16 ✓. Both points lie on the circle.
Question 2: A circle has center (3, −1) and passes through the point (7, 2). What is the area of the circle?
- 5π
- 25π (Correct answer)
- √25 π
- 10π
Correct answer: 25π
Radius = √((7−3)² + (2−(−1))²) = √(16+9) = √25 = 5. Area = π(5²) = 25π.
Question 3: A chord of a circle with radius 10 is 12 units long. How far is the chord from the center?
- 8 (Correct answer)
- 6
- √(10²−12²)
- 4
Correct answer: 8
The perpendicular from the center bisects the chord into two segments of 6 each. Distance = √(10² − 6²) = √(100−36) = √64 = 8.
Question 4: What is the length of the arc intercepted by a central angle of 2π/3 radians in a circle with diameter 18?
- 6π (Correct answer)
- 3π
- 12π
- 9π
Correct answer: 6π
Radius = 9. Arc length = rθ = 9 × (2π/3) = 6π.
Question 5: The circle x² + y² + 4x − 12y + 15 = 0 has center (h, k). What is h + k?
- −2 + 6 = 4 (Correct answer)
- 8
- −8
- 2
Correct answer: −2 + 6 = 4
Complete the square: (x+2)² − 4 + (y−6)² − 36 + 15 = 0 → (x+2)² + (y−6)² = 25. Center = (−2, 6), so h + k = −2 + 6 = 4.
Question 6: Two tangent segments are drawn to a circle from an external point P. One tangent touches the circle at A and the other at B. If the arc AB (the minor arc) measures 100°, what is the measure of angle P?
- 50°
- 80° (Correct answer)
- 100°
- 40°
Correct answer: 80°
The major arc AB = 360° − 100° = 260°. Angle P = (1/2)|major arc − minor arc| = (1/2)(260° − 100°) = (1/2)(160°) = 80°.
Question 7: A circle has radius 4. A sector of this circle has a perimeter of 4π + 8. What is the central angle of the sector in radians?
- π (Correct answer)
- π/2
- 2π/3
- π/3
Correct answer: π
Perimeter of sector = arc length + 2 radii = 4θ + 8 = 4π + 8, so 4θ = 4π and θ = π.
Bluebook SAT Test Circles 9
The equation of a circle is (x − 4)² + (y − 4)² = 16.
Which of the following points lies on the circle?