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Circles — arcs, sectors, angles, equations — ACT practice questions

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Practice 58 Circles — arcs, sectors, angles, equations questions in the app

What this topic is

On the ACT Mathematics test, Circles — arcs, sectors, angles, equations covers radius, circumference, area, arc measure, sector area, central and inscribed angles, and the standard circle equation in the coordinate plane.

Sample questions

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Question 1Easier

In the standard $(x,y)$ coordinate plane, a circle has center $(-3,4)$ and radius 5. Which of the following is an equation of the circle?

A$(x-3)^2+(y+4)^2=25$✗ Not this oneB$(x+3)^2+(y-4)^2=5$✗ Not this oneC$(x-3)^2+(y+4)^2=5$✗ Not this oneD$(x+3)^2+(y-4)^2=25$✓ Correct

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Answer: D — $(x+3)^2+(y-4)^2=25$

A circle with center $(h,k)$ and radius $r$ has equation $(x-h)^2+(y-k)^2=r^2$. With $h=-3$, $k=4$, and $r=5$, this is $(x+3)^2+(y-4)^2=25$.

Question 2Easier

A sector of a circle with radius 6 has central angle $60^\circ$. What is the area of the sector?

A$2\pi$✗ Not this oneB$6\pi$✓ CorrectC$12\pi$✗ Not this oneD$36\pi$✗ Not this one

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Answer: B — $6\pi$

Sector area $=\dfrac{60}{360}\pi r^2=\dfrac{1}{6}\pi(36)=6\pi$.

Question 3Easier

A circle has a circumference of $10\pi$ units. What is the area of the circle, in square units?

A$5\pi$✗ Not this oneB$10\pi$✗ Not this oneC$20\pi$✗ Not this oneD$25\pi$✓ Correct

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Answer: D — $25\pi$

From $2\pi r=10\pi$, the radius is 5. Therefore, the area is $\pi r^2=25\pi$ square units.

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