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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. The equation x² + y² − 6x + 2y − 6 = 0 represents a circle. What is the radius?

    Answer: Both A and C

    Completing the square: (x−3)² − 9 + (y+1)² − 1 − 6 = 0 → (x−3)² + (y+1)² = 16. Radius = 4 = √16. Both A and C are equivalent.

  2. Point P is outside a circle of radius 7. A tangent from P touches the circle at T and the distance PT = 24. What is the distance from P to the center O?

    Answer: Both B and C

    OT ⊥ PT (radius to tangent point), so PO² = PT² + OT² = 576 + 49 = 625. PO = 25 = √625. Both B and C are equivalent.

  3. A circle has center (0, 0) and radius r. A horizontal line y = 3 is tangent to the circle. What is r?

    Answer: 3

    A line is tangent to a circle when the distance from the center to the line equals the radius. Distance from (0,0) to y=3 is 3, so r = 3.

  4. What is the area of the region inside circle (x−1)² + (y−1)² = 9 but outside circle (x−1)² + (y−1)² = 4?

    Answer: 5π

    Radii are √9 = 3 and √4 = 2. Area of annulus = π(3² − 2²) = π(9−4) = 5π.

  5. A central angle of 72° subtends an arc. If the radius of the circle is 5, what is the area of the sector?

    Answer: 5π

    Sector area = (θ/360°)·πr² = (72/360)·π(25) = (1/5)(25π) = 5π.

  6. An inscribed angle in a circle intercepts an arc of 160°. What is the measure of the inscribed angle?

    Answer: 80°

    An inscribed angle equals half the intercepted arc: 160°/2 = 80°.

  7. The circle x² + y² = 100 intersects the positive x-axis and positive y-axis at points A and B respectively. What is the length of chord AB?

    Answer: 10√2

    A = (10, 0) and B = (0, 10). AB = √((10−0)² + (0−10)²) = √(100+100) = 10√2.