# Circles on the SAT: Examples & Practice | 1600.now Source: https://1600.now/sat-skill/circles --- Math · Geometry and Trigonometry ## Circles Read a circle's radius before using area or circumference. For arcs and sectors, use the angle's fraction of a full turn; for a coordinate equation, read the center and radius from standard form. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### Read the center from the subtracted coordinates The equation $(x-2)^2+(y+3)^2=25$ describes a circle centered at $(2,-3)$ with radius 5. Standard form is $(x-h)^2+(y-k)^2=r^2$, so the right side gives the squared radius. The signs inside the parentheses are opposite the center coordinates. To verify the center, substitute it: both squared terms become zero. To verify a point on the circle, their sum must equal 25. ### Find area and circumference from the radius A circle with diameter 12 has radius 6. Its area is $A=\pi r^2=36\pi$, and its circumference is $C=2\pi r=12\pi$. Area and circumference answer different questions and have different units. Doubling the radius doubles circumference but quadruples area. If an area is multiplied by 9, the radius is multiplied by 3, not 9. ### Use a fraction of a turn for arcs and sectors A 60-degree central angle is $\frac{60}{360}=\frac16$ of a full circle. For radius 6, its arc length is $\frac16(12\pi)=2\pi$, and its sector area is $\frac16(36\pi)=6\pi$. The arc uses circumference; the sector uses area. A central angle has its vertex at the center. An inscribed angle intercepting the same arc is half the central angle, so identify the vertex before using the number. ### Use radians directly when they are given With an angle $\theta$ in radians, arc length is $s=r\theta$ and sector area is $A=\frac12r^2\theta$. For $r=6$ and $\theta=\frac\pi3$, those formulas again give $2\pi$ and $6\pi$. Do not insert a degree measure into these radian formulas. Convert degrees using $\theta_{\text{radians}}=\theta_{\text{degrees}}\cdot\frac\pi{180}$, or use the fraction-of-360 method instead. ### Check your understanding Try it yourself: What is the radius of $(x+1)^2+(y-4)^2=49$? · A $1$ B $4$ C $7$ D $49$ ### Sample circles questions Circles · Easy A circle has a radius of $17$ meters. What is the area, in square meters, of the circle? A $\frac{17\pi}{2}$ B $\frac{17\pi}{1}$ C $\frac{34\pi}{1}$ D $\frac{289\pi}{1}$ - [Open the question and explanation](https://1600.now/bank/math/32be24f3) Circles · Easy Circle M has a radius of 32 millimeters (mm). What is the area of circle M, in $\text{mm}^2$? A $32\pi$ B $64\pi$ C $128\pi$ D $1,024\pi$ - [Open the question and explanation](https://1600.now/bank/math/68deaef8) Circles · Easy A circle in the $xy$-plane has the equation $(x-11)^{2}+(y-k)^{2}=49$. Which of the following gives the center of the circle and its radius? A The center is at $(11, k)$ and the radius is 7. B The center is at $(k, 11)$ and the radius is 7. C The center is at $(k, 11)$ and the radius is 49. D The center is at $(11, k)$ and the radius is 49. - [Open the question and explanation](https://1600.now/bank/math/f68d69e7) ### Practice this skill 1. Label radius, diameter, and the angle vertex before calculating. 2. Choose circumference for arcs and area for sectors. 3. Check a coordinate-circle answer by substituting a known point. [Practice circles](https://1600.now/bank/math/skill/Circles) [Print the circles worksheet and worked answers](https://1600.now/sat-circles-worksheet). Then use a [mixed practice module](https://1600.now/modules) to check whether you can choose this method among other question types. ### Source and question labels The bank label for this guide is "Circles" in Geometry and Trigonometry. The worked examples above are written for this guide. - [College Board: Types of Math tested](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Area and Volume](https://1600.now/sat-skill/area-and-volume)** Choose the formula for the requested quantity, then identify its perpendicular height and units. - **[Right Triangles and Trigonometry](https://1600.now/sat-skill/right-triangles-and-trig)** Locate the right angle first. - **[Lines, Angles, and Triangles](https://1600.now/sat-skill/lines-angles-triangles)** Name the geometric relationship before writing an equation.