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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 center of the circle x² + y² − 10x + 4y + 20 = 0?

    Answer: (5, −2)

    Complete the square: (x−5)²+(y+2)² = 25+4−20 = 9; center (5,−2).

  2. A central angle of π/6 radians corresponds to how many degrees?

    Answer: 30°

    (π/6)(180°/π) = 180°/6 = 30°.

  3. A circle has diameter 14. What is its area?

    Answer: 49π

    r = 14/2 = 7; area = π(7)² = 49π.

  4. An arc subtends a central angle of 5π/6 radians in a circle of radius 6. What is the arc length?

    Answer: 5π

    s = rθ = 6·(5π/6) = 5π.

  5. Two inscribed angles in the same circle intercept the same arc. What is the relationship between the two angles?

    Answer: They are equal

    Inscribed angles that intercept the same arc are equal (both equal half the arc measure).

  6. A circle has area 64π. How long is an arc that subtends a central angle of 45°?

    Answer: 2π

    r² = 64 → r = 8; arc = (45/360)(2π·8) = (1/8)(16π) = 2π.

  7. The circle (x + 4)² + (y − 1)² = 36 has been graphed. Which point lies on the circle?

    Answer: (−4, 7)

    For (−4, 7): (−4+4)² + (7−1)² = 0 + 36 = 36 ✓.