MathFree

Circles — SAT practice questions

Circles on the SAT Math test covers circumference, radius, central angles, arc length, chords, and angles in standard position given in radians. A student has to find arc length from a circumference such as 36π and a central angle of 120°, find chord length when the radius is 6, and work from an angle measuring (3π)/4. Questions are multiple choice with four answer choices or student-produced response and often include a diagram. Common traps are mixing degrees and radians, using radius in place of diameter, and confusing arc length with sector area, so the choices usually include those nearby wrong values.

Section: Math 44 questions on the paper
136 practice questions in the app

Sample questions

Question 1

In a circle with center $C$ , points $A$ and $B$ lie on the circle and $\angle ACB=90^\circ$ . The radius of the circle is 6. What is the length of chord $\overline{AB}$ ?

A6
B $6\sqrt{2}$
C9
D12

Show answer

Answer: B — $6\sqrt{2}$

$\triangle ACB$ is an isosceles right triangle with legs 6, so $AB=6\sqrt{2}$ .

Question 2

A circle has circumference $36\pi$ . An arc of the circle has a central angle of $120^\circ$ . What is the length of the arc?

A $6\pi$
B $9\pi$
C $12\pi$
D $18\pi$

Show answer

Answer: C — $12\pi$

\dfrac{120}{360}\cdot36\pi=12\pi

Question 3

An angle in standard position has measure $\dfrac{3\pi}{4}$ . What is the value of $\sin \dfrac{3\pi}{4}$ ?

A $\dfrac{\sqrt{2}}{2}$
B $-\dfrac{\sqrt{2}}{2}$
C $\sqrt{2}$
D $-\sqrt{2}$

Show answer

Answer: A — $\dfrac{\sqrt{2}}{2}$

The angle $\dfrac{3\pi}{4}$ is in Quadrant II, where sine is positive. Its reference angle is $\dfrac{\pi}{4}$ , so $\sin \dfrac{3\pi}{4}=\dfrac{\sqrt{2}}{2}$ .

Practice 136 Circles questions in the app

Circles — SAT practice questions

Sample questions

More SAT topics

Math