Strategy #16: Apply Circle Theorems

Category: Geometry

Key circle facts for the SAT:

• Arc measure refers to the angular distance between two points on a circle. It is equal to the central angle that intercepts it.

• Arc length refers to the linear distance between two points on a circle. It is equal to: (central angle / 360°) × circumference

• Sector area = (central angle / 360°) × area of the circle

• An inscribed angle is half the central angle that subtends the same arc

• A radius drawn to a point of tangency is perpendicular to the tangent line

Why it matters: Circle problems appear on nearly every SAT and often combine arc length with algebra or the equation of a circle.

Practice tip: For any circle problem, identify what you know: radius, diameter, arc, chord, central angle, or inscribed angle. Then write the formula that connects what you know to what you need.