Bluebook SAT Test Circles 5

Question 1

What is the radius of the circle x² + y² − 8x − 6y + 21 = 0?

Accepted Answer

2

Answer

Complete the square: (x−4)²+(y−3)²=16+9−21=4; radius = √4 = 2.

Question 2

A sector of a circle with radius 12 has a central angle of 2π/3 radians. What is its area?

Accepted Answer

48π

Answer

A = ½r²θ = ½(144)(2π/3) = 72·(2π/3) = 48π.

Question 3

A chord connects two points on a circle of radius 10, and its perpendicular bisector passes through the center. The midpoint of the chord is 6 units from the center. What is the chord's length?

Accepted Answer

16

Answer

Half-chord = √(r²−d²) = √(100−36) = √64 = 8; full chord = 16.

Question 4

A circle with center (0,0) passes through the point (−5, 12). What is the area of the circle?

Accepted Answer

169π

Answer

r = √(25 + 144) = √169 = 13; area = π(13)² = 169π.

Question 5

An angle inscribed in a circle measures 42°. What is the measure of the arc it intercepts?

Accepted Answer

84°

Answer

The intercepted arc = 2 × inscribed angle = 2 × 42° = 84°.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Circles 5