Bluebook SAT Test Circles 6 — Questions and Answers
Question 1: Write the equation of a circle with center (7, −3) and radius 4.
- (x − 7)² + (y + 3)² = 16 (Correct answer)
- (x + 7)² + (y − 3)² = 16
- (x − 7)² + (y − 3)² = 16
- (x − 7)² + (y + 3)² = 4
Correct answer: (x − 7)² + (y + 3)² = 16
Standard form: (x−7)²+(y−(−3))²=4² → (x−7)²+(y+3)²=16.
Question 2: A circle has a central angle of 240° and a radius of 3. What is the arc length?
- 4π (Correct answer)
- 8π
- 6π
- 2π
Correct answer: 4π
Arc = (240/360)(2π·3) = (2/3)(6π) = 4π.
Question 3: An inscribed angle of 65° intercepts an arc. The central angle subtending the same arc is:
- 130° (Correct answer)
- 65°
- 32.5°
- 195°
Correct answer: 130°
Central angle = 2 × inscribed angle = 2 × 65° = 130°.
Question 4: The diameter of a circle is the chord passing through the center. If an inscribed angle intercepts the diameter, what is the angle's measure?
- 90° (Correct answer)
- 180°
- 45°
- 60°
Correct answer: 90°
The diameter subtends a semicircle (180°), and an inscribed angle is half the arc = 90° (Thales' theorem).
Question 5: Rewrite x² + y² + 12x − 16y + 75 = 0 in standard form. What is the radius?
- 5 (Correct answer)
- 75
- √75
- 10
Correct answer: 5
(x+6)²+(y−8)²=36+64−75=25; radius=√25=5.
Question 6: Two tangent lines from an external point each touch a circle of radius 5. The distance from the external point to the center is 13. What is the length of each tangent segment?
- 12 (Correct answer)
- 8
- √194
- √120
Correct answer: 12
Tangent is perpendicular to radius at the point of tangency; length = √(13²−5²) = √(169−25) = √144 = 12.
Question 7: A circle has equation (x−2)²+(y+6)²=r². The point (6, −6) lies on the circle. What is r?
- 4 (Correct answer)
- 16
- 8
- 2
Correct answer: 4
(6−2)²+(−6+6)²=16+0=16, so r²=16, r=4.
Bluebook SAT Test Circles 6
Write the equation of a circle with center (7, −3) and radius 4.