Circle Secrets Reference Sheet
CIRCLE SECRETS
Name:
Date:
Radius (r): Center to edge
Diameter (d): Across circle (d = 2r)
Pi (π): ≈ 3.14
Degrees: Total 360°
Circumference
With d
\[ C = \pi d \]
With r
\[ C = 2 \pi r \]
Area
Square Units
\[ A = \pi r^2 \]
If given d, divide by 2 first!
Arc Length (s)
Fraction of Edge
\[ s = \left( \frac{\theta}{360} \right) \cdot 2 \pi r \]
Angle Relationships
Central
\[ \angle = \text{Arc} \]
Inscribed
\[ \angle = \frac{\text{Arc}}{2} \]
Vertex Inside
\[ \angle = \frac{\text{Arc}_1 + \text{Arc}_2}{2} \]
Vertex Outside
\[ \angle = \frac{\text{Big} - \text{Small}}{2} \]
Inscribed Polygon
Opposite angles are supplementary
\[ \angle_1 + \angle_2 = 180^\circ \]
Pro Tip
Always identify the vertex position first!
On? Divide by 2. Outside? Subtract and divide by 2. Center? Angle = Arc.
Essential Check
- Radius = ½ Diameter
- Circle = 360°
