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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. A circle passes through the origin. Its center is at (5, 0). What is the equation of the circle?

    Answer: (x−5)² + y² = 25

    The radius = distance from (5,0) to (0,0) = 5. Equation: (x−5)² + y² = 25.

  2. In a circle, an inscribed angle measures 47°. Another inscribed angle intercepts the same arc. What is its measure?

    Answer: 47°

    Inscribed angles that intercept the same arc are equal in measure.

  3. A circle has circumference C. What is the area of the circle in terms of C?

    Answer: C²/(4π)

    C = 2πr so r = C/(2π). Area = πr² = π(C/(2π))² = πC²/(4π²) = C²/(4π).

  4. The circle (x−2)² + (y+3)² = r² passes through the point (−1, 1). What is r²?

    Answer: 25

    r² = (−1−2)² + (1−(−3))² = (−3)² + 4² = 9 + 16 = 25.

  5. Two circles have radii in the ratio 2:5. The area of the smaller circle is 12π. What is the area of the larger circle?

    Answer: 75π

    Area ratio = (2:5)² = 4:25. If smaller area = 12π, larger = 12π × (25/4) = 75π.

  6. A sector has a central angle of 3π/4 radians and arc length 9π/2. What is the radius?

    Answer: 6

    Arc length = rθ, so 9π/2 = r × (3π/4). r = (9π/2) ÷ (3π/4) = (9π/2) × (4/(3π)) = 6.

  7. A circle has center O and radius 10. Chord AB has length 16. What is the distance from O to the midpoint of AB?

    Answer: Both A and C

    The perpendicular from O to chord AB meets AB at its midpoint, and the distance = √(10² − 8²) = √(100−64) = √36 = 6. Both answer A (6) and answer C (√36 = 6) are correct.