Bluebook SAT Test Circles 9

Question 1

The equation of a circle is (x − 4)² + (y − 4)² = 16. Which of the following points lies on the circle?

Accepted Answer

Both A and B

Answer

(4−4)² + (8−4)² = 0 + 16 = 16 ✓; (8−4)² + (4−4)² = 16 + 0 = 16 ✓. Both points lie on the circle.

Question 2

A circle has center (3, −1) and passes through the point (7, 2). What is the area of the circle?

Accepted Answer

25π

Answer

Radius = √((7−3)² + (2−(−1))²) = √(16+9) = √25 = 5. Area = π(5²) = 25π.

Question 3

A chord of a circle with radius 10 is 12 units long. How far is the chord from the center?

Accepted Answer

8

Answer

The perpendicular from the center bisects the chord into two segments of 6 each. Distance = √(10² − 6²) = √(100−36) = √64 = 8.

Question 4

What is the length of the arc intercepted by a central angle of 2π/3 radians in a circle with diameter 18?

Accepted Answer

6π

Answer

Radius = 9. Arc length = rθ = 9 × (2π/3) = 6π.

Question 5

The circle x² + y² + 4x − 12y + 15 = 0 has center (h, k). What is h + k?

Accepted Answer

−2 + 6 = 4

Answer

Complete the square: (x+2)² − 4 + (y−6)² − 36 + 15 = 0 → (x+2)² + (y−6)² = 25. Center = (−2, 6), so h + k = −2 + 6 = 4.

Bluebook SAT Practice Test