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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 (x − 1)² + (y + 7)² = 25 represents a circle. What are the center and radius?

    Answer: Center (1, −7), radius 5

    Standard form (x−h)²+(y−k)²=r²: h=1, k=−7, r=√25=5.

  2. A circle has area 100π. What is the diameter?

    Answer: 20

    A = πr² = 100π → r² = 100 → r = 10 → diameter = 20.

  3. An arc length of 6π is cut from a circle of radius 9. What is the central angle in radians?

    Answer: 2π/3

    Arc = rθ → 6π = 9θ → θ = 6π/9 = 2π/3.

  4. What is the area of a sector with radius 5 and central angle π/2 radians?

    Answer: 25π/4

    Sector area = (1/2)r²θ = (1/2)(25)(π/2) = 25π/4.

  5. An inscribed angle intercepts a semicircle (arc of 180°). What is the measure of the inscribed angle?

    Answer: 90°

    An inscribed angle is half the intercepted arc: 180°/2 = 90° (Thales' theorem).

  6. Rewrite x² + y² − 4x + 8y + 4 = 0 in standard form and identify the center.

    Answer: Center (2, −4)

    Complete the square: (x²−4x+4)+(y²+8y+16) = −4+4+16 = 16; center is (2, −4).

  7. A wheel has radius 3 feet. How far does the wheel travel in one full rotation?

    Answer: 6π feet

    One full rotation = circumference = 2πr = 2π(3) = 6π feet.