Description
Return squared center-to-point distance minus radius squared as power.
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 squared center-to-point distance minus radius squared as power.
When to use this tool
Use Triangle Circumcenter Power At Point when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter point, center, radius. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read power. Use the output convention below.
Require two-dimensional point and center arrays and nonnegative radius. Return squared center-to-point distance minus radius squared as power.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| point | Point | Required. Array of finite number; maximum items 256. |
| center | Center | Required. Array of finite number; maximum items 256. |
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| power | Power | Required. Finite number. |
{
"input": {
"point": [
3,
4
],
"center": [
0,
0
],
"radius": 3
},
"output": {
"power": 16
}
}Limitations and assumptions
- Coordinates and radius share units and power uses squared-length units; negative is inside, zero on, and positive outside the supplied circle, without locating a triangle circumcenter.
- 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 Radical Axis Signed Residual
Compute point power for each circle and return left power minus right power.
- Circle External Tangent Length Squared Gap
Return distance²-radius² and exists when that value is nonnegative.