Circle Secrets Reference Sheet
Circle Secrets
Name:
Date:
RADIUS (r)
Center to edge
Diameter (d)
\[ d = 2r \]
Pi (π)
≈ 3.14
Degrees
Total 360°
Circumference
With D: \[ C = \pi d \]
With R: \[ C = 2 \pi r \]
Area
\[ A = \pi r^2 \]
If given d, divide by 2!
Arc Length
Fraction of Edge
\[ s = \frac{\theta}{360} \cdot 2 \pi r \]
Inscribed Polygons
A B C D
\[ \angle A + \angle C = 180^\circ \]
\[ \angle B + \angle D = 180^\circ \]
Opposite angles are supplementary.
Angle Relationships
Central
\[ \angle = \text{Arc} \]
Inscribed
\[ \angle = \frac{\text{Arc}}{2} \]
∠
Vertex Inside
\[ \angle = \frac{\text{Arc}_{\small 1} + \text{Arc}_{\small 2}}{2} \]
∠
Vertex Outside
\[ \angle = \frac{\text{Big} - \text{Small}}{2} \]
Right Triangle
Angle in semi-circle is exactly 90°.
PRO TIP: Vertex position identifies the formula.
ON: ÷ 2 OUT: Sub then ÷ 2 IN: Add then ÷ 2
Radius = 1/2 Diameter
Circle = 360° Total
