Bluebook SAT Test Circles 16

Question 1

A circle with center O has an inscribed polygon ABCD. If arc AB = 80°, arc BC = 100°, and arc CD = 70°, what is the measure of arc DA?

Accepted Answer

110°

Answer

All arcs must sum to 360°: arc DA = 360° − 80° − 100° − 70° = 110°.

Question 2

A line y = mx + b is tangent to the circle x² + y² = r² from the outside. Which condition must hold?

Accepted Answer

b² = r²(1 + m²)

Answer

The distance from origin to y = mx + b is |b|/√(1+m²) = r, so b² = r²(1+m²).

Question 3

A circle has area A and circumference C. Which expression is equal to the radius?

Accepted Answer

Both A and B

Answer

C = 2πr → r = C/(2π); A = πr² → r = √(A/π). Both expressions equal r.

Question 4

Circle O has diameter AB. Point C lies on the circle. If angle CAB = 35°, what is angle ABC?

Accepted Answer

55°

Answer

Angle ACB = 90° (angle in semicircle). So angle ABC = 180° − 90° − 35° = 55°.

Question 5

A circle with radius 5 is centered at the origin. A point P on the circle is in the first quadrant, and the radius to P makes a 37° angle with the positive x-axis. What are the coordinates of P? (Use sin 37° ≈ 0.6, cos 37° ≈ 0.8)

Accepted Answer

Both A and C

Answer

P = (5·cos37°, 5·sin37°) = (5·0.8, 5·0.6) = (4, 3). Both A and C are equivalent.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Circles 16