Bluebook SAT Test Circles 13

Question 1

Circle C has center (2, −3) and is tangent to the y-axis. What is the radius of the circle?

Accepted Answer

2

Answer

The distance from the center (2, −3) to the y-axis (x = 0) is |2| = 2, which equals the radius.

Question 2

A circular pizza with diameter 16 inches is cut into 8 equal slices. What is the area of each slice?

Accepted Answer

8π

Answer

Total area = π(8)² = 64π. Each slice = 64π/8 = 8π square inches.

Question 3

A circle is inscribed in a square with side length 10. What is the area of the region inside the square but outside the circle?

Accepted Answer

100 − 25π

Answer

The inscribed circle has radius 5. Its area = 25π. Area outside = 100 − 25π.

Question 4

In a circle, an arc measures 4π and the radius is 6. What fraction of the circle's circumference does this arc represent?

Accepted Answer

1/3

Answer

Circumference = 2π(6) = 12π. Fraction = 4π/12π = 1/3.

Question 5

A circle with center O has points A and B on it. The central angle AOB = 120° and OA = 9. What is the length of chord AB?

Accepted Answer

9√3

Answer

Using the law of cosines: AB² = 9² + 9² − 2(9)(9)cos(120°) = 81 + 81 − 162(−1/2) = 162 + 81 = 243. AB = √243 = 9√3.

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