Circles — SAT practice questions

Math
44 questions on the paper
136 practice questions in the app
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Practice 136 Circles questions in the app

What this topic is

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.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

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 $\overline{AB}$ ?

6✗ Not this one

6\sqrt{2}

✓ Correct9✗ Not this one12✗ Not this one

Show answer

Answer: B — $6\sqrt{2}$

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

Question 2Easier

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?

6\pi

✗ Not this one

9\pi

✗ Not this one

12\pi

✓ Correct

18\pi

✗ Not this one

Show answer

Answer: C — $12\pi$

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

Question 3Easier

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

\dfrac{\sqrt{2}}{2}

✓ Correct

-\dfrac{\sqrt{2}}{2}

✗ Not this one

\sqrt{2}

✗ Not this one

-\sqrt{2}

✗ Not this one

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 $\sin \dfrac{3\pi}{4}=\dfrac{\sqrt{2}}{2}$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 136 Circles questions in the app

Circles — SAT practice questions

What this topic is

Sample questions

More SAT topics

Math