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C# code to derive tangential points between two circles to create a trapezoid

Submitted by: @import:stackexchange-codereview·Mar 10, 2026·

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derivecreatepointscirclestwobetweentrapezoidcodetangential

Problem

These are the steps to determine coordinates of the 4 points (P1, P2, P3, P4) that make up a tangential trapezoid connecting to circles. Another way of looking at it is to think of the tangential segments of being the parts of a belt that would not be wrapped around the pulleys. The math should work regardless of the orientation of the two circles in coordinate space.

Code (usage @ bottom):

```
internal class TrapezoidBuilder
{
private const double RadiansToDegrees = 180/Math.PI;
private readonly double _bufferDistanceC0;
private readonly double _bufferDistanceC1;

private readonly Point _pointC0;
private readonly Point _pointC1;
public TrapezoidPoints TrapezoidPoints;

public TrapezoidBuilder(Point pointC0, Point pointC1, double bufferDistanceC0, double bufferDistanceC1)
{
_pointC0 = pointC0;
_pointC1 = pointC1;
_bufferDistanceC0 = bufferDistanceC0;
_bufferDistanceC1 = bufferDistanceC1;

TrapezoidPoints = new TrapezoidPoints();

CalculateTrapezoidPoints();
}

public void CalculateTrapezoidPoints()
{
// Get the angle of the line C0-C1 in degrees. This will be used in conjunction with angleA to determine the vector of these points
double angleRelativeToPositiveXAxis = CalculateAngleRelativeToXAxis(_pointC0, _pointC1);

// Get angleA
double angleA = CalculateAngleA(_pointC0, _pointC1, _bufferDistanceC0, _bufferDistanceC1);

//// Calculate P1 and P2 coordinates first

double positiveAngle = angleRelativeToPositiveXAxis + angleA;

double cosPositiveAngle = Math.Cos(positiveAngle/RadiansToDegrees);

double valueToAddToC0X = cosPositiveAngle*_bufferDistanceC0;

// Set P1's X coordinate
TrapezoidPoints.P1.X = _pointC0.X + valueToAddToC0X;

double valueToAddToC1X = cosPositiveAngle*_bufferDistanceC1;

// Set P2's X coordinate
TrapezoidPoints.P2.X = _pointC1.X + valueToAddToC1X;

Solution

It's not clear to me what are buffer0 and buffer1? If these represent the radius values (like C1-P1 line for buffer1), then perhaps radius0 (and radius1) would be a better name here.

I'd create and use a data class for each point-radius pair. Say, InputPoint class with Point and Radius or something similar.

I'd separate constructor and results. The results are calculations that should not be part of the constructor. Take, for example, the class named UriBuilder in .NET: you can construct it, change the inputs, and only when you call the property named Uri - you get the calculated uri. The same should apply here, too. Constructing a class gives us an instance with a valid state. Calculations - in their own methods or property-getters (that are practically methods, by the way). So TrapezoidPoints should be the returned type of a GetTrapezoid method (or maybe TryGetTrapezoid if this pattern apply here), and not part of the class' state.

Context

StackExchange Code Review Q#11858, answer score: 2

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