SAT Questions: Circles

The SAT (Scholastic Assessment Test) is a standardized test widely used for college admissions in the United States. It is administered by the College Board and is designed to assess a student’s readiness for college.

The Digital SAT is a new, computer-based version of the SAT exam that was introduced by the College Board in 2023. The Digital SAT uses a multistage adaptive testing model: Each section (Reading and Writing, Math) is divided into two modules. The difficulty of the second module depends on the student’s performance in the first module.

The following diagram shows the circle equations, formulas, and properties that you must be familiar when preparing for the SAT. Scroll down the page for more examples and solutions SAT questions that involve circles and circle theorems.

Core Formulas:

1. Circumference:
   C = 2πr (where r is the radius)
   C = πd (where d is the diameter)
   
2. Area:
   A = πr² (where r is the radius)

Important Concepts and Relationships:

1. Relationship between Radius and Diameter:
   d = 2r
   
2. Central Angles, Arcs, and Sectors:
   Understanding how central angles relate to the length of arcs and the area of sectors is crucial.
   

Arc Length:
Arc Length = (central angle/360°) × 2πr

Sector Area:
Sector Area = (central angle/360°) × πr²

Equation of a Circle:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.

SAT Circle Equations
Question:
If the point (-2,8) lies on a circle with a center at (-2,4), which of the following is an equations of the circle?

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Circle equations — Harder example
Question:
A circle in the xy-plane has its center at (7,14). If the point (7,34) lies on the circle, which of the is an equation of the circle?

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Circles
Arcs and Sectors

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Math SAT Practice: Exam 1 - Question 6
Area of circle

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Math SAT Practice: Exam 1 Question 10
Circle - area, circumference

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