Circles
Circle questions on the SAT split into geometry and coordinate-plane algebra. Start by spotting the radius, center, or angle rule the problem uses.
核心知识
Circle problems on the SAT split into two flavors: geometric (arcs, angles, sectors) and algebraic (equations in the coordinate plane). Both rely on the radius as the key link.
深入理解
Rule: Circle questions split into geometric and coordinate-form algebra.
- Geometry problems use arcs, sectors, tangents, and circle angle rules.
- Algebra problems use
( 𝑥 − ℎ ) 2 + ( 𝑦 − 𝑘 ) 2 = 𝑟 2 - The radius is the common link between both styles.
Start by deciding which version of the circle the problem is using, then use the radius or center immediately.
知识点教程
9Use circle definitions and basic properties (radius, diameter, chords) to relate lengths.
Radius, diameter, and chord questions usually turn into a right triangle from the center to a chord.
Use tangent properties (tangent is perpendicular to radius at point of tangency) when relevant.
A tangent meets a circle once, and the radius to that point is perpendicular. That right angle is th
Use circle angle relationships (central/inscribed angles; chords/tangents) when relevant.
Central angles equal their intercepted arcs, and inscribed angles are half the same arc. A diameter
Solve problems involving arcs, arc length, and sector area.
Arc length and sector area are fractions of a full circle. Match the formula to degrees or radians b
Convert between degrees and radians when needed (SAT).
Degrees and radians are just two ways to write the same angle. Convert with the standard pi-based fa
Use the unit circle or special-angle reasoning to connect angles and coordinates (SAT).
On the unit circle, coordinates come from cosine and sine. Special angles and quadrant signs give th
Work with circle equations in the coordinate plane (center-radius form).
Center-radius form shows the center and radius at a glance. Flip the signs inside the parentheses, a
Rewrite circle equations by completing the square.
Use completing the square to turn expanded circle equations into center-radius form. That reveals th
Use the distance formula to connect a point on the circle to its radius.
The distance formula and the circle equation express the same relationship. Use the center and one p