Bluebook SAT Test Circles 8

Question 1

A circle passes through points (0,0), (6,0), and (0,8). What is the radius of the circle?

Accepted Answer

5

Answer

The hypotenuse of the right triangle formed is √(6²+8²)=10, which is the diameter, so r=5.

Question 2

The equation of a circle is x² + y² − 2x + 4y − 20 = 0. What is the area of this circle?

Accepted Answer

25π

Answer

(x−1)²+(y+2)²=20+1+4=25; r=5; area=25π.

Question 3

A circle has radius r. A sector with central angle 2π/5 is cut out. What fraction of the circle's area does the sector represent?

Accepted Answer

1/5

Answer

Fraction = θ/(2π) = (2π/5)/(2π) = 1/5.

Question 4

What is the length of the longest chord of a circle with area 36π?

Accepted Answer

12

Answer

r=6; the longest chord is the diameter = 2r = 12.

Question 5

In a circle, a central angle intercepts an arc of 150°. What is the central angle in radians?

Accepted Answer

5π/6

Answer

150° × π/180° = 150π/180 = 5π/6.

Bluebook SAT Practice Test