Description
Require centralAngle in [0, 2π] radians and return half that angle.
Circle calculations distinguish radius, diameter, chord, sagitta, tangent, and oriented offsets. Branch choices determine signs and which arc or segment is meant; a scalar identity does not always establish an actual geometric construction.
Require centralAngle in [0, 2π] radians and return half that angle.
When to use this tool
Use Circle Tangent Chord Angle when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter centralAngle. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read tangentChordAngle. Use the output convention below.
Require centralAngle in [0, 2π] radians and return half that angle.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| centralAngle | Central Angle | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| tangentChordAngle | Tangent Chord Angle | Required. Finite number. |
{
"input": {
"centralAngle": 1.5707963267948966
},
"output": {
"tangentChordAngle": 0.7853981633974483
}
}Limitations and assumptions
- The supplied angle determines the selected tangent/chord branch, which can exceed π/2; this is not automatically the acute unoriented angle and no actual tangent, chord, or arc choice is verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Construct the circles, chord, or segment in coordinates when existence or orientation matters. Use the complete geometry and an appropriate tolerance for intersection or tangency decisions.
References
Similar or alternative tools
- Circle Common Chord Midpoint Offset
Return (d²+r1²-r2²)/(2d) along the first-to-second center axis and sqrt(max(0, r1²-offset²)) for halfChord.
- Circle External Tangent Length Squared Gap
Return distance²-radius² and exists when that value is nonnegative.