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?

The center is at $(11, k)$ and the radius is 7.

The center is at $(k, 11)$ and the radius is 7.

The center is at $(k, 11)$ and the radius is 49.

The center is at $(11, k)$ and the radius is 49.

Math · Geometry and Trigonometry

Circles

Circle equations, arcs, sectors, inscribed angles, and tangent lines.

What the SAT Tests

Digital SAT circle questions include the equation of a circle in the coordinate plane, arc length and sector area in radians, and inscribed-angle relationships.

Key Tips for Circles

The equation (x−h)² + (y−k)² = r² gives center and radius directly.
Complete the square to convert a general circle equation into center-radius form.
Arc length = rθ and sector area = ½r²θ, both with θ in radians.

How to recognize Circles questions

Look for Geometry and Trigonometry signals: equations, graphs, tables, variables, units, or words that describe a relationship.
Before solving, decide whether the answer should be a value, expression, coordinate, graph feature, or interpretation.
The official College Board skill label is Circles; match your practice misses to that label when reviewing.

Fast solving workflow

Translate the givens into an equation, graph, table, or labeled diagram before using answer choices.
Choose the fastest method: mental math for one-step work, paper algebra for clean symbolic steps, Desmos for intersections/tables/roots, and substitution for ordered answer choices.
Check the final answer against the question stem, especially units, signs, and whether it asks for x, y, a sum, a coefficient, or an interpretation.

Common traps

Assuming a diagram is to scale instead of proving the relationship.
Using the wrong radius, diameter, height, or angle measure in a formula.
Forgetting that similar figures preserve ratios, not raw side lengths.

Sample Circles Questions

These are real practice questions pulled from our Digital SAT bank. Try each one before reading the highlighted correct answer.

Question 1 · Easy
A circle has a radius of $17$ meters. What is the area, in square meters, of the circle?
- A. $\frac{17 π}{2}$
- B. $\frac{17 π}{1}$
- C. $\frac{34 π}{1}$
- D. $\frac{289 π}{1}$ Correct
Question 2 · Easy
Circle M has a radius of 32 millimeters (mm). What is the area of circle M, in $mm^{2}$ ?
- A. $32 π$
- B. $64 π$
- C. $128 π$
- D. $1, 024 π$ Correct
Question 3 · Easy
A circle in the $x y$ -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.Correct
- 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.

Practice Circles Questions

Drill circles questions in the Digital SAT Math question bank, or take a full-length practice module to see how this skill appears under test conditions.

Practice block	What to do	Move on when
Warmup	Solve 10 untimed circles questions and write the rule used for each.	You can explain 8 of 10 without reading the explanation.
Timed drill	Solve 20 filtered bank questions at real module pace.	Accuracy is at least 80% and misses are not repeating.
Transfer	Take a mixed timed module and mark each Geometry and Trigonometry miss.	The skill still holds up when mixed with other question types.

FAQs

What is Circles on the Digital SAT?

Digital SAT circle questions include the equation of a circle in the coordinate plane, arc length and sector area in radians, and inscribed-angle relationships.

How hard are circles questions?

Circles questions appear at every difficulty level on the Digital SAT Math section. The hardest versions gate access to the top scaled scores in the hard Module 2.

How do I practice circles?

Use the 1600.now question bank to filter for circles questions, solve at least 20 in a row, and review every miss with the written explanation.

Related Math Skills

SAT® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this product.

AboutPrivacyTermsResourcesContact