Circle Theorems Calculator
Apply six circle relations. Angles use degrees; lengths use one shared unit.
Formula
α=a/2; α=90°; α=180°−a; c=2√(a²−b²); α=(a−b)/2; t=√(a²−b²).
Angle (°) or length ≈ (120)÷2
How to use
- Choose the relation.
- Enter a and b using the table; unused fields are ignored.
- Read the requested angle or length.
Examples
- A cyclic quadrilateral angle of 56° has opposite angle 124°.
Input guide
| Relation | a | b |
|---|---|---|
| Inscribed | Central angle (°) | Unused |
| Thales | Unused | Unused |
| Cyclic | Known interior angle (°) | Unused |
| Chord | Radius | Center-to-chord distance |
| Secants | Far arc (°) | Near arc (°) |
| Tangent | Point-to-center distance | Radius |
Frequently asked questions
Which angle does Thales give?
The angle subtended by a diameter is 90°. Other angle modes exclude 0° and straight angles.
Which lengths are valid?
Chord mode needs radius a>b≥0; tangent mode needs point-center distance a>radius b>0.
How are secant arcs entered?
a is the far arc and b the near arc: a>b and a+b<360°.
Sources
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