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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 points (0,0), (6,0), and (0,8). What is the radius of the circle?

    Answer: 5

    The hypotenuse of the right triangle formed is √(6²+8²)=10, which is the diameter, so r=5.

  2. The equation of a circle is x² + y² − 2x + 4y − 20 = 0. What is the area of this circle?

    Answer: 25π

    (x−1)²+(y+2)²=20+1+4=25; r=5; area=25π.

  3. A circle has radius r. A sector with central angle 2π/5 is cut out. What fraction of the circle's area does the sector represent?

    Answer: 1/5

    Fraction = θ/(2π) = (2π/5)/(2π) = 1/5.

  4. What is the length of the longest chord of a circle with area 36π?

    Answer: 12

    r=6; the longest chord is the diameter = 2r = 12.

  5. In a circle, a central angle intercepts an arc of 150°. What is the central angle in radians?

    Answer: 5π/6

    150° × π/180° = 150π/180 = 5π/6.

  6. Two circles are concentric (same center). The outer circle has radius 10 and the inner circle has radius 6. What is the area of the ring (annulus) between them?

    Answer: 64π

    Area = π(10²) − π(6²) = 100π − 36π = 64π.

  7. A circle has equation (x−3)²+(y+2)²=50. The point (3+t, −2) lies on the circle. What is the positive value of t?

    Answer: 5√2

    (3+t−3)²+(−2+2)²=50 → t²=50 → t=√50=5√2.