Bluebook SAT Test Circles 5 — Questions and Answers
Question 1: What is the radius of the circle x² + y² − 8x − 6y + 21 = 0?
- 2 (Correct answer)
- 4
- √21
- 8
Correct answer: 2
Complete the square: (x−4)²+(y−3)²=16+9−21=4; radius = √4 = 2.
Question 2: A sector of a circle with radius 12 has a central angle of 2π/3 radians. What is its area?
- 48π (Correct answer)
- 24π
- 16π
- 96π
Correct answer: 48π
A = ½r²θ = ½(144)(2π/3) = 72·(2π/3) = 48π.
Question 3: A chord connects two points on a circle of radius 10, and its perpendicular bisector passes through the center. The midpoint of the chord is 6 units from the center. What is the chord's length?
- 16 (Correct answer)
- 8
- 12
- 20
Correct answer: 16
Half-chord = √(r²−d²) = √(100−36) = √64 = 8; full chord = 16.
Question 4: A circle with center (0,0) passes through the point (−5, 12). What is the area of the circle?
- 169π (Correct answer)
- 144π
- 25π
- 13π
Correct answer: 169π
r = √(25 + 144) = √169 = 13; area = π(13)² = 169π.
Question 5: An angle inscribed in a circle measures 42°. What is the measure of the arc it intercepts?
- 84° (Correct answer)
- 42°
- 21°
- 138°
Correct answer: 84°
The intercepted arc = 2 × inscribed angle = 2 × 42° = 84°.
Question 6: A circle has circumference 30π. What is the area of a sector with central angle 120°?
- 225π/3
- 75π (Correct answer)
- 150π
- 50π
Correct answer: 75π
C=30π → r=15; area = (120/360)π(225) = (1/3)(225π) = 75π.
Question 7: Which of the following equations represents a circle with the largest radius?
- (x−1)²+(y−1)²=100 (Correct answer)
- x²+y²=81
- (x+3)²+(y−2)²=49
- (x−5)²+y²=64
Correct answer: (x−1)²+(y−1)²=100
The radii are √100=10, √81=9, √49=7, √64=8; the largest is 10.
Bluebook SAT Test Circles 5
What is the radius of the circle x² + y² − 8x − 6y + 21 = 0?