Description
Compute sqrt(radius²-(chord/2)²) using scaled alternatives where needed and apply the positiveBranch sign.
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.
Compute sqrt(radius²-(chord/2)²) using scaled alternatives where needed and apply the positiveBranch sign.
When to use this tool
Use Chord Apothem Sign Branch when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter radius, chordLength, positiveBranch. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedApothem. Use the output convention below.
Require nonnegative radius and chordLength with half chord no greater than radius. Compute sqrt(radius²-(chord/2)²) using scaled alternatives where needed and apply the positiveBranch sign.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; minimum 0. |
| chordLength | Chord Length | Required. Finite number; minimum 0. |
| positiveBranch | Positive Branch | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedApothem | Signed Apothem | Required. Finite number. |
{
"input": {
"radius": 5,
"chordLength": 6,
"positiveBranch": true
},
"output": {
"signedApothem": 4
}
}Limitations and assumptions
- This is the signed center-to-chord apothem under a caller-selected side; no geometric orientation, chord endpoint, or actual circle is inspected.
- 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
- Chord Sagitta Curvature Sensitivity
Return 8 × sagitta/(chord²+4 × sagitta²) and its derivative with respect to sagitta.
- Chord Sagitta Residual
Compute the minor sagitta using its rationalized expression and return measuredSagitta minus expectedSagitta.