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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 has equation (x + 3)² + (y − 5)² = 49. Which transformation maps this circle to the unit circle x² + y² = 1?

    Answer: Translate (3,−5), then dilate by factor 1/7

    First shift center (−3, 5) to origin by translating (+3, −5), giving x² + y² = 49, then shrink radius 7 to 1 by scaling by 1/7.

  2. A wheel of radius 2 feet rolls along a flat road without slipping. How far has the center of the wheel traveled after the wheel makes 5 complete rotations?

    Answer: 20π feet

    Each rotation the wheel travels one circumference = 2π(2) = 4π feet. Five rotations = 5 × 4π = 20π feet.

  3. In a circle with radius 13, a chord is drawn 5 units from the center. What is the length of the chord?

    Answer: Both B and C

    Half-chord = √(13²−5²) = √(169−25) = √144 = 12. Full chord = 24. Both B and C are equal.

  4. Circle O has center (0, 0) and radius 5. Line y = 3 intersects the circle. What are the x-coordinates of the intersection points?

    Answer: ±4

    Substituting y = 3: x² + 9 = 25, so x² = 16 and x = ±4.

  5. A sector has radius 6 and central angle 150°. What is the area of the sector?

    Answer: 15π

    Area = (150/360) × π(6)² = (5/12) × 36π = 15π.

  6. The diameter of a circle is the segment from (−4, 1) to (6, 1). What is the equation of the circle?

    Answer: (x−1)² + (y−1)² = 25

    Center = midpoint = ((−4+6)/2, (1+1)/2) = (1, 1). Radius = distance from center to endpoint = √((6−1)²+0²) = 5. Equation: (x−1)² + (y−1)² = 25.

  7. In a circle with center O and radius r, two radii OA and OB form a central angle of 90°. What is the length of chord AB in terms of r?

    Answer: r√2

    With OA = OB = r and angle AOB = 90°, triangle OAB is an isosceles right triangle. AB = r√2.