Description
Validate three noncollinear two-dimensional vertices with A distinct from B and C.
Triangle identities relate side lengths, angles, and special points under a nondegenerate geometric model. A contribution to a point or a local ratio is different from constructing the complete point or proving that supplied values form a triangle.
Validate three noncollinear two-dimensional vertices with A distinct from B and C.
When to use this tool
Use Geometry: Triangle Angle Bisector Foot when you need an explicit triangle identity or local construction.
How to use the tool and how it works
- Enter vertexA, vertexB, vertexC. 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 result. Expand result to inspect the returned fields.
Validate three noncollinear two-dimensional vertices with A distinct from B and C. Compute AB and AC with the linked distance calculator, then interpolate along B-to-C at AB/(AB+AC), returning foot and oppositeSideFraction inside result.1
The linked distance operation supplies AB and AC, the side lengths that determine the internal-bisector division ratio.2
The linked linear interpolation operation constructs each coordinate between B and C with parameter AB/(AB+AC).3
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vertexA | Vertex A | Required. Array of finite number. Implementation limit: 128 items. |
| vertexB | Vertex B | Required. Array of finite number. Implementation limit: 128 items. |
| vertexC | Vertex C | Required. Array of finite number. Implementation limit: 128 items. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated members; expand to inspect the fields below. | Required. Object. |
| result.foot | Two-dimensional internal-bisector point on BC in the input coordinate unit. | Calculated result member: array. |
| result.oppositeSideFraction | Parameter AB/(AB+AC) measured from B toward C. | Calculated result member: number. |
{
"input": {
"vertexA": [
0,
0
],
"vertexB": [
3,
0
],
"vertexC": [
0,
4
]
},
"output": {
"result": {
"foot": [
1.7142857142857142,
1.7142857142857142
],
"oppositeSideFraction": 0.42857142857142855
}
}
}Limitations and assumptions
- This is the internal angle bisector from vertexA under Euclidean planar coordinates; equality and noncollinearity checks are exact and finite precision can limit extreme coordinates.
- Outputs are nested inside result. 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 triangle from coordinates or solve the complete geometric constraints when consistency matters. Match side ordering, angle units, and internal-versus-external conventions to the intended identity.
References
Similar or alternative tools
- Triangle Isogonal Cevian Ratio
Return (adjacentFirst/adjacentSecond)²/firstRatio.
- Triangle Altitude Foot Parameter
Use scaled coordinates and a normalized B-to-C direction to project A onto its supporting line, returning parameter and foot coordinates.