Circle Basics and Equations

Vocabulary flashcards covering the fundamental formulas and equations related to circles, including area, circumference, sectors, and the standard coordinate equation.

Diameter of a Circle

The distance across a circle through its center, calculated using the formula $d = 2r$.

Circumference of a Circle

The linear distance around the edge of a circle, calculated using the formula $C = 2\text{π}r$.

Area of a Circle

The total space contained within a circle, calculated using the formula $A = \text{π}r^2$.

Arc Length

The distance along the curved line of a circle's arc, calculated as $\text{Arc Length} = \frac{\theta}{360^\text{∘}} \times 2\text{π}r$.

Area of a Sector

The area of a portion of a circle defined by two radii and an arc, calculated as $\text{Area of a Sector} = \frac{\theta}{360^\text{∘}} \times \text{π}r^2$.

Inscribed Angle

An angle formed by two chords in a circle that have a common endpoint, measured as $\frac{\text{Intercepted Arc}}{2}$.

Standard Equation of a Circle

An algebraic way to describe a circle on a coordinate plane, expressed as $(x - h)^2 + (y - k)^2 = r^2$.

Center of a Circle (Standard Equation)

The fixed point from which all points on the circle are equidistant, represented by the coordinates $(h, k)$ in the standard equation.

Radius of a Circle (Standard Equation)

The constant distance from the center to any point on the circle, represented by the variable $r$ in the standard equation.