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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. Write the equation of a circle with center (7, −3) and radius 4.

    Answer: (x − 7)² + (y + 3)² = 16

    Standard form: (x−7)²+(y−(−3))²=4² → (x−7)²+(y+3)²=16.

  2. A circle has a central angle of 240° and a radius of 3. What is the arc length?

    Answer: 4π

    Arc = (240/360)(2π·3) = (2/3)(6π) = 4π.

  3. An inscribed angle of 65° intercepts an arc. The central angle subtending the same arc is:

    Answer: 130°

    Central angle = 2 × inscribed angle = 2 × 65° = 130°.

  4. The diameter of a circle is the chord passing through the center. If an inscribed angle intercepts the diameter, what is the angle's measure?

    Answer: 90°

    The diameter subtends a semicircle (180°), and an inscribed angle is half the arc = 90° (Thales' theorem).

  5. Rewrite x² + y² + 12x − 16y + 75 = 0 in standard form. What is the radius?

    Answer: 5

    (x+6)²+(y−8)²=36+64−75=25; radius=√25=5.

  6. Two tangent lines from an external point each touch a circle of radius 5. The distance from the external point to the center is 13. What is the length of each tangent segment?

    Answer: 12

    Tangent is perpendicular to radius at the point of tangency; length = √(13²−5²) = √(169−25) = √144 = 12.

  7. A circle has equation (x−2)²+(y+6)²=r². The point (6, −6) lies on the circle. What is r?

    Answer: 4

    (6−2)²+(−6+6)²=16+0=16, so r²=16, r=4.