Circles Flashcards

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

Answer: 2

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

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

Answer: 8π

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

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?

Answer: 100 − 25π

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

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

Answer: 1/3

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

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?

Answer: 9√3

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.

What is the equation of the circle with center (0, 0) that passes through (−3, 4)?

Answer: x² + y² = 25

Radius = √((−3)² + 4²) = √(9+16) = 5. Equation: x² + y² = 25.

The area of a circle is increased by 44%. By what percentage is the radius increased?

Answer: 20%

New area = 1.44πr². New radius = √(1.44)r = 1.2r. The radius increases by 20%.