Work with arcs, sectors, angles, chords and tangents, and the equation of a circle in the coordinate plane. It is part of Geometry and Trigonometry in the Math section. The book teaches it in Chapter 28, Circles, with 12 practice questions, and tests it 2 more times across the two full-length practice tests.
About Chapter 28
Circle questions on the digital SAT draw on a short list of ideas: area and circumference, arcs and sectors as fractions of a whole circle, radian measure, the equation of a circle in the xy-plane, and two angle facts about tangents and inscribed angles. Most errors come from mixing up radius and diameter, or arc and sector, rather than from hard algebra, so the method below keeps those apart.
What the question looks like
Find an area or a circumference from a radius or a diameter, often for a wheel, a track or a garden bed.
Find an arc length or a sector area from a central angle given in degrees or radians.
Convert an angle between degrees and radians.
Read the center and radius from an equation, write an equation from a center and a point, or complete the square to put an equation in standard form.
Use an angle fact: an inscribed angle, an angle inscribed in a semicircle, or a tangent line meeting a radius.
Student-produced responses cannot include π, so a question may say that a length or area "is kπ" and ask for k.
How to recognize it
"Radius," "diameter," "around," or "one full revolution": C = 2πr and A = πr^2
A central angle and "arc," or the distance along part of a circle: Arc length as a fraction of the circumference
A central angle and a region, slice or watered area: Sector area as a fraction of the circle's area
π in an angle measure, or the word "radians": π radians = 180°
An equation with x^2 and y^2 that have equal coefficients: Circle equation; complete the square if needed
"Tangent": The radius to the point of tangency is perpendicular to the tangent
An angle whose vertex is on the circle: Inscribed angle = half its intercepted arc
Common traps
Using the diameter as the radius: The problem gives a width across the circle
Mixing up arc length and sector area: A length is asked for (path, edge, distance), or an area (region, bed, watered)
Dividing the angle by 180 instead of 360: You are finding a fraction of the whole circle
Using s = rθ with degrees: The angle has a ° symbol, so convert it or use θ/360
Copying the center's signs from the equation: (x − h) means the x-coordinate is h, so (x + 2) means −2
Reporting r^2 as the radius: The right side of standard form is the radius squared
Making an inscribed angle equal the arc: The vertex is on the circle, so take half
Treating a tangent segment as the hypotenuse: The hypotenuse is the segment from the center to the outside point
Video lessons
Two short lessons from independent YouTube creators, chosen for this skill. The notes are ours; the videos belong to their creators, who are not affiliated with this site.
Every circle rule, worked through (Penguin SAT Prep , 14:06). Watch for: Arc length, sector area, and radians.
The circle equation in the xy-plane (Settele Tutoring — SAT® Lessons and Strategies, 3:57). Watch for: Completing the square to find the center and radius.
Practice this skill
The full method, worked examples and 12 practice questions with every answer choice explained are in Chapter 28 of the book and in the study workspace, where an AI coach can talk you through each one.
Skill by Skill Prep is independent. SAT® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this website or book. Bluebook™ is a trademark of the College Board. Desmos is a trademark of Desmos Studio PBC. Practice results and ranges are study estimates, not official scores or admission predictions.