Math

Circles — SAT practice questions

139 practice questions in the app
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Practice 139 Circles questions in the app

What this topic is

Circles questions cover equations in the xy-plane, arcs, sectors, chords and radian measure.

The standard form (x - h) squared plus (y - k) squared equals r squared gives the center and radius; when an equation arrives expanded, completing the square in both x and y recovers that form. An arc or sector is the same fraction of the whole circle as its central angle is of a full turn, so a quarter of the angle means a quarter of the circumference.

Radians measure angles by arc length on a circle of radius one, and a full turn is two pi radians.

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 $∠ A C B = 9 0^{\circ}$ . The radius of the circle is 6. What is the length of chord $\overline{A B}$ ?

6✗ Not this one

6 \sqrt{2}

✓ Correct9✗ Not this one12✗ Not this one

Show answer

Answer: B — $6 \sqrt{2}$

$△ A C B$ is an isosceles right triangle with legs 6, so $A B = 6 \sqrt{2}$ .

Question 2Easier

A circle has circumference $36 π$ . An arc of the circle has a central angle of $12 0^{\circ}$ . What is the length of the arc?

6 π

✗ Not this one

9 π

✗ Not this one

12 π

✓ Correct

18 π

✗ Not this one

Show answer

Answer: C — $12 π$

\frac{120}{360} \cdot 36 π = 12 π

Question 3Easier

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

\frac{\sqrt{2}}{2}

✓ Correct

- \frac{\sqrt{2}}{2}

✗ Not this one

\sqrt{2}

✗ Not this one

- \sqrt{2}

✗ Not this one

Show answer

Answer: A — $\frac{\sqrt{2}}{2}$

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

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Practice 139 Circles questions in the app

Circles — SAT practice questions

What this topic is

Sample questions

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Math