SAT Circles Guide: Every Formula and Trap
How to solve every SAT circle question, from basic circumference to standard-form equations with a completing-the-square step.
The Circle Equation
The standard form of a circle is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.
Completing the Square
When the SAT gives you a circle equation in expanded form, you'll need to complete the square on both the x and y terms to rewrite it in standard form. Then the center and radius fall out.
Arcs and Sectors
Arc length = (θ/360) × 2πr for degrees, or θ × r for radians. Sector area = (θ/360) × πr² for degrees, or (θ/2) × r² for radians.
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