Description
Return (adjacentFirst/adjacentSecond)²/firstRatio.
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.
Return (adjacentFirst/adjacentSecond)²/firstRatio.
When to use this tool
Use Triangle Isogonal Cevian Ratio when you need an explicit triangle identity or local construction.
How to use the tool and how it works
- Enter adjacentFirst, adjacentSecond, firstRatio. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read isogonalRatio. Use the output convention below.
Require positive adjacentFirst, adjacentSecond, and firstRatio. Return (adjacentFirst/adjacentSecond)²/firstRatio.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| adjacentFirst | Adjacent First | Required. Finite number; strictly above 0. |
| adjacentSecond | Adjacent Second | Required. Finite number; strictly above 0. |
| firstRatio | First Ratio | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| isogonalRatio | Isogonal Ratio | Required. Finite number. |
{
"input": {
"adjacentFirst": 6,
"adjacentSecond": 3,
"firstRatio": 2
},
"output": {
"isogonalRatio": 2
}
}Limitations and assumptions
- The ratio convention uses the two opposite-side segments in the order corresponding to the adjacent sides; no actual triangle, cevian, segment positions, or isogonal relationship is verified.
- 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
- Geometry: Triangle Angle Bisector Foot
Validate three noncollinear two-dimensional vertices with A distinct from B and C.
- Triangle Median Ratio
Return their ratio and vertexToCentroid-2 × centroidToMidpoint as twoToOneResidual.