Using B4XCanvas and DrawCircle, and geometry laws, we can test whether two given circles intersect or not.

If they intersect the points of intersections are returned.

The intersection points (if they exist) can be calculated as follows:

You can call this function and then draw the intersection points on the canvas:

If they intersect the points of intersections are returned.

### Circle Equations

Assuming two circles with:The intersection points (if they exist) can be calculated as follows:

**Calculate Distance Between Circle Centers**:

**Check for Intersection**:**Calculate Intersection Points**:- Calculate a and h, which determine the position of the intersection points.
- Determine the points P2 as the base point on the line between the centers of the circles:
- Find the offset points to get the intersection points:

B4X:

```
Sub FindIntersectionPoints(x1 As Double, y1 As Double, r1 As Double, x2 As Double, y2 As Double, r2 As Double) As List
Dim result As List
result.Initialize
Dim d As Double = Sqrt(Power(x2 - x1, 2) + Power(y2 - y1, 2))
' Check if circles intersect
If d > r1 + r2 Or d < Abs(r1 - r2) Then
Log("No intersection points.")
Return result
End If
' Calculate a and h
Dim a As Double = (Power(r1, 2) - Power(r2, 2) + Power(d, 2)) / (2 * d)
Dim h As Double = Sqrt(Power(r1, 2) - Power(a, 2))
' Calculate the base point on the line between the circles' centers
Dim x3 As Double = x1 + a * (x2 - x1) / d
Dim y3 As Double = y1 + a * (y2 - y1) / d
' Calculate the two intersection points
Dim x4_1 As Double = x3 + h * (y2 - y1) / d
Dim y4_1 As Double = y3 - h * (x2 - x1) / d
Dim x4_2 As Double = x3 - h * (y2 - y1) / d
Dim y4_2 As Double = y3 + h * (x2 - x1) / d
' Add the points to the result list
result.Add(CreateMap("x" : x4_1, "y" : y4_1))
result.Add(CreateMap("x" : x4_2, "y" : y4_2))
Return result
End Sub
```

You can call this function and then draw the intersection points on the canvas:

B4X:

```
Sub DrawIntersections
Dim x1 As Double = 100, y1 As Double = 100, r1 As Double = 75
Dim x2 As Double = 150, y2 As Double = 100, r2 As Double = 75
Dim intersections As List = FindIntersectionPoints(x1, y1, r1, x2, y2, r2)
Dim cvs As B4XCanvas
cvs.Initialize(mainForm.rootPane)
cvs.DrawCircle(x1, y1, r1, xui.Color_Blue, False, 2dip)
cvs.DrawCircle(x2, y2, r2, xui.Color_Red, False, 2dip)
For Each p As Map In intersections
Dim px As Double = p.Get("x")
Dim py As Double = p.Get("y")
cvs.DrawCircle(px, py, 5dip, xui.Color_Green, True, 1dip)
Next
cvs.Refresh
End Sub
```

#### Attachments

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