Bluebook SAT Test Circles 11

Question 1

The equation x² + y² − 6x + 2y − 6 = 0 represents a circle. What is the radius?

Accepted Answer

Both A and C

Answer

Completing the square: (x−3)² − 9 + (y+1)² − 1 − 6 = 0 → (x−3)² + (y+1)² = 16. Radius = 4 = √16. Both A and C are equivalent.

Question 2

Point P is outside a circle of radius 7. A tangent from P touches the circle at T and the distance PT = 24. What is the distance from P to the center O?

Accepted Answer

Both B and C

Answer

OT ⊥ PT (radius to tangent point), so PO² = PT² + OT² = 576 + 49 = 625. PO = 25 = √625. Both B and C are equivalent.

Question 3

A circle has center (0, 0) and radius r. A horizontal line y = 3 is tangent to the circle. What is r?

Accepted Answer

3

Answer

A line is tangent to a circle when the distance from the center to the line equals the radius. Distance from (0,0) to y=3 is 3, so r = 3.

Question 4

What is the area of the region inside circle (x−1)² + (y−1)² = 9 but outside circle (x−1)² + (y−1)² = 4?

Accepted Answer

5π

Answer

Radii are √9 = 3 and √4 = 2. Area of annulus = π(3² − 2²) = π(9−4) = 5π.

Question 5

A central angle of 72° subtends an arc. If the radius of the circle is 5, what is the area of the sector?

Accepted Answer

5π

Answer

Sector area = (θ/360°)·πr² = (72/360)·π(25) = (1/5)(25π) = 5π.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Circles 11