Description
Return distance²-radius² and exists when that value is nonnegative.
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 distance²-radius² and exists when that value is nonnegative.
When to use this tool
Use Circle External Tangent Length Squared Gap when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter distance, radius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read squaredLength, exists. Inspect exists before interpreting the associated values.
Require nonnegative distance and radius. Return distance²-radius² and exists when that value is nonnegative.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| distance | Distance in the stated common unit and geometric model. | Required. Finite number; minimum 0. |
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| squaredLength | Squared Length | Required. Finite number. |
| exists | Exists | Required. Boolean. |
{
"input": {
"distance": 5,
"radius": 3
},
"output": {
"squaredLength": 16,
"exists": true
}
}Limitations and assumptions
- Distance is from point to circle center and equality permits a zero-length tangent; inside points return a negative square diagnostically, without constructing a tangent or verifying geometry.
- 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 Tangent Chord Angle
Require centralAngle in [0, 2π] radians and return half that angle.
- Geometry: Circle Tangent Radius Dot Check
Dot their separately normalized components and compare its absolute value inclusively with tolerance inside result.