Circle1

(x-h)^2 + (y-k)^2 = r^2

Circle2

(x-m)^2 + (y-n)^2 = s^2

Where h,k,m and n are the respective centres offset from the zero origin and
r and s are the respective radii.

With pen and paper I can get the result by solving the two equations
simultaneously using the algebra method I learnt 35 years ago. The algebra
method involves a fair bit of expression manipulation before getting to the
point of being able to solve for x and then for y. To manipulate these
expressions in VB code seems rather complex so I figured there must be some
other method that can be used.

As an alternative I tried placing the two circle expressions in a For/Next
loop with a Step value of 0.0001 and incrementing  'y' in both expressions
by the Step amount until Cirlcle1 'x' value approximately matches Circle2
'x' value. This method returned some results but proved to be unreliable and
slow.

I would  be most appreciative if some of you Math/Code fundies could point
me in the right direction with this problem.

TIA

line (h-r, k-r) - (h+r, k+r), , b
line (m-s, n-s) - (m+s, n+s), , b

Or maybe start by seeing if sqr((h-m)^2 + (k-n)^2) <= (r+s)

http://www.sonoma.edu/users/w/wilsonst/papers/geometry/circles/

'This calculates the intersection points of two overlapping circles
''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
Private Sub FindIntercepts()
Dim XintersectA As Single 'first  x intersect
Dim YintersectA As Single 'first y intersect
Dim XintersectB As Single 'second  x intersect
Dim YintersectB As Single 'second y intersect
Dim d, r, s, h, k, m, n As Single ' intermediate variables to make
expression easier to write and follow
Dim CheckOverLap As Boolean
r = R1
s = R2
h = Centre1X
k = Centre1Y
m = Centre2X
n = Centre2Y
d = Sqr((((m - h) ^ 2) + ((n - k) ^ 2)))

        If Sqr((h - m) ^ 2 + (k - n) ^ 2) <= (r + s) Then ' Check for
overlap to avoid run time error
        CheckOverLap = True

        'expression to find the XintersectA value
        ''''''
         XintersectA = ((m + h) / 2) + ((m - h) * ((r ^ 2) - (s ^ 2))) / (2
* (d ^ 2)) + (((n - k) / (2 * (d ^ 2))) * Sqr(((((r + s) ^ 2) - (d ^ 2)) *
((d ^ 2) - ((s - r) ^ 2)))))

        'expression to find the YintersectA value
        '''''
        YintersectA = ((n + k) / 2) + ((n - k) * ((r ^ 2) - (s ^ 2))) / (2 *
(d ^ 2)) - (((m - h) / (2 * (d ^ 2))) * Sqr(((((r + s) ^ 2) - (d ^ 2)) * ((d
^ 2) - ((s - r) ^ 2)))))

        'expression to find the XintersectB value
        '''''
        XintersectB = ((m + h) / 2) + ((m - h) * ((r ^ 2) - (s ^ 2))) / (2 *
(d ^ 2)) - (((n - k) / (2 * (d ^ 2))) * Sqr(((((r + s) ^ 2) - (d ^ 2)) * ((d
^ 2) - ((s - r) ^ 2)))))

        'expression to find the YintersectB value
        '''''
        YintersectB = ((n + k) / 2) + ((n - k) * ((r ^ 2) - (s ^ 2))) / (2 *
(d ^ 2)) + (((m - h) / (2 * (d ^ 2))) * Sqr(((((r + s) ^ 2) - (d ^ 2)) * ((d
^ 2) - ((s - r) ^ 2)))))

        Pic2.Cls
        Pic2.Print " First X intersect         = " & Round(XintersectA, 2)
        Pic2.Print " First Y intersect         = " & Round(YintersectA, 2)
        Pic2.Print ""
        Pic2.Print " Second X intersect   = " & Round(XintersectB, 2)
        Pic2.Print " Second Y intersect   = " & Round(YintersectB, 2)
        Pic2.Print ""

        Else
        Pic2.Print " Overlap =  " & CheckOverLap
        MsgBox ("No overlap of circles.   Cannot solve."), , ("Intercept
Check")
        End If

Pic1.ForeColor = vbYellow
Pic1.Circle (XintersectA, YintersectA), 0.3
Pic1.Circle (XintersectB, YintersectB), 0.3

End Sub