Circle Theorems Explorer
Drag points around the circle to explore fundamental circle theorems. Watch angles update in real-time and see the relationships come alive.
Theorem
Measurements
| Angle 1 | -- |
| Angle 2 | -- |
| Relation | -- |
| Arc | -- |
Circle Theorems Explained
Key Theorems
- Inscribed Angle: An angle formed by two chords is half the central angle subtending the same arc
- Central Angle: Angle at the center is twice the inscribed angle on the same arc
- Semicircle: Any angle inscribed in a semicircle is a right angle (90°)
- Tangent-Radius: A tangent to a circle is perpendicular to the radius at the point of contact
- Cyclic Quadrilateral: Opposite angles sum to 180°
Formulas
- Inscribed angle: θ = α/2 (where α is central angle)
- Central angle: α = 2θ
- Arc length: s = rθ (θ in radians)
- Sector area: A = (1/2)r²θ
- Chord length: c = 2r·sin(θ/2)
Applications
- Navigation and surveying
- Architecture and design
- Computer graphics
- Astronomy and orbital mechanics
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