Bluebook SAT Test Circles 15

Question 1

The graph of x² + (y − k)² = 25 is tangent to the x-axis. What are the possible values of k?

Accepted Answer

k = ±5

Answer

The circle is tangent to the x-axis when the distance from center (0, k) to x-axis equals the radius: |k| = 5, so k = ±5.

Question 2

A circle has circumference 16π. What is the area of a sector with arc length 4π?

Accepted Answer

16π

Answer

Radius = 8. Fraction of circle = 4π/16π = 1/4. Sector area = (1/4)·π(8²) = (1/4)(64π) = 16π.

Question 3

The center of a circle is at (3, 4) and the circle is tangent to the line x = −1. What is the radius?

Accepted Answer

4

Answer

Distance from center (3, 4) to the line x = −1 is |3 − (−1)| = 4, which is the radius.

Question 4

In a circle with center O, chord AB is perpendicular to radius OC at point D, where D is the midpoint of AB. If OC = 10 and OD = 6, what is AB?

Accepted Answer

Both B and C

Answer

AD = √(OA² − OD²) = √(100−36) = 8. AB = 16. Both B and C are equivalent (√64 × 2 = 16).

Question 5

Which of the following points is inside the circle (x − 1)² + (y + 2)² = 20?

Accepted Answer

(4, 1)

Answer

For (4,1): (4−1)²+(1+2)² = 9+9 = 18 < 20 ✓ (inside). For (5,−2): 16+0=16<20 — also inside. For (1,3): 0+25=25>20. For (−2,2): 9+16=25>20. The first listed inside point is (4,1).

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Circles 15