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Circles Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. What is the radius of the circle x² + y² − 8x − 6y + 21 = 0?

    Answer: 2

    Complete the square: (x−4)²+(y−3)²=16+9−21=4; radius = √4 = 2.

  2. A sector of a circle with radius 12 has a central angle of 2π/3 radians. What is its area?

    Answer: 48π

    A = ½r²θ = ½(144)(2π/3) = 72·(2π/3) = 48π.

  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?

    Answer: 16

    Half-chord = √(r²−d²) = √(100−36) = √64 = 8; full chord = 16.

  4. A circle with center (0,0) passes through the point (−5, 12). What is the area of the circle?

    Answer: 169π

    r = √(25 + 144) = √169 = 13; area = π(13)² = 169π.

  5. An angle inscribed in a circle measures 42°. What is the measure of the arc it intercepts?

    Answer: 84°

    The intercepted arc = 2 × inscribed angle = 2 × 42° = 84°.

  6. A circle has circumference 30π. What is the area of a sector with central angle 120°?

    Answer: 75π

    C=30π → r=15; area = (120/360)π(225) = (1/3)(225π) = 75π.

  7. Which of the following equations represents a circle with the largest radius?

    Answer: (x−1)²+(y−1)²=100

    The radii are √100=10, √81=9, √49=7, √64=8; the largest is 10.

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Sources & references

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  1. satsuite.collegeboard.org — Score release, test delivery, time limit, test dates, fees, registration, retake policy · verified Oct 2026
  2. bluebook.collegeboard.org — Test delivery · verified Oct 2026