Circle Secrets Cheat Sheet
Circle Secrets
Master Reference Document
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Date:
Radius (r): Center to edge
Diameter (d): Across circle (d = 2r)
Pi (π): ≈ 3.14
Total Degrees: 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
\[ s = \frac{\theta}{360} \cdot 2\pi r \]
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
\[ \angle = \frac{\text{Big Arc} - \text{Small Arc}}{2} \]
Pro Tip
Always identify the vertex position first! On edge? Divide by 2. Outside? Subtract and divide by 2. Center? Angle = Arc.
Essential Check
• Radius = Half of Diameter
• Total Circle = 360° Degrees
Circle Secrets • Master Tool Geometry Reference v3.7
