Circles
Circle equations, geometric properties, arcs, angles, and tangent lines
Circle questions cover equations, geometric properties, arcs, radians, and tangent lines.
Why this matters
The SAT tests circles from five different angles: reading the equation, applying geometric properties, working with arcs and radians, checking points, and finding tangent slopes.
The five patterns
Circle Equation
Identify the center and radius from a circle equation, or build the equation from given information. Watch the signs — (x − 3) means the center is at 3, not −3.
›Geometric Properties
How radii, chords, tangents, and inscribed shapes relate to each other. Pure geometry — no equation needed.
›Arcs, Angles & Radians
Central angles, arc lengths, and converting between degrees and radians. The key ratio: arc length = radius × angle (in radians).
›Applying Equations
Use the circle equation to check if a point lies on the circle or to find coordinates that satisfy it. Substitute and verify.
›Tangent Lines
Find the slope of a tangent line using the fact that it is perpendicular to the radius at the point of tangency.
The biggest trap: mixing up r and r². If the equation says (x − 2)² + (y + 5)² = 49, the radius is 7, not 49. The SAT consistently offers both as answer choices.