Circles
Circle equations, geometric properties, arcs, angles, and tangent lines
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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.