Description
Return (d²+r1²-r2²)/(2d) along the first-to-second center axis and sqrt(max(0, r1²-offset²)) for halfChord.
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.
Return (d²+r1²-r2²)/(2d) along the first-to-second center axis and sqrt(max(0, r1²-offset²)) for halfChord.
When to use this tool
Use Circle Common Chord Midpoint Offset when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter firstRadius, secondRadius, centerDistance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read offset, halfChord. Use the output convention below.
Require positive radii and centerDistance satisfying touching or intersecting circle bounds. Return (d²+r1²-r2²)/(2d) along the first-to-second center axis and sqrt(max(0, r1²-offset²)) for halfChord.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstRadius | First Radius | Required. Finite number; strictly above 0. |
| secondRadius | Second Radius | Required. Finite number; strictly above 0. |
| centerDistance | Center Distance | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| offset | Signed displacement or phase under the convention above. | Required. Finite number. |
| halfChord | Half Chord | Required. Finite number. |
{
"input": {
"firstRadius": 5,
"secondRadius": 5,
"centerDistance": 6
},
"output": {
"offset": 3,
"halfChord": 4
}
}Limitations and assumptions
- Coincident centers are rejected and tangencies yield zero half chord; lengths share units and no actual points, axis orientation, or measurement tolerance are inferred.
- 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
- Geometry: Circle Radial Offset Curvature
Return that offsetRadius and its reciprocal as curvature inside result.
- Circle Tangent Chord Angle
Require centralAngle in [0, 2π] radians and return half that angle.