C(UV) denotes the circle with diameter UV.
T(P,QR) denotes the tangential distance PS,
where point P lies outside C(QR), point S
lies on C(QR), and PS is tangent to C(QR).
Let A, B, C, and D be distinct, collinear
points in that order.
Construct a point E on line AD such that
EF = T(E,AB) = T(E,CD) = EG
Consider an x axis where A is at 0, and B,E,C, and D are at x values of B,E,C, and D.
With a little help from Pythagoras:
(E  B/2)^2  (B/2)^2 = (CE + (DC)/2)^2  ((DC)/2)^2
Which leads to:
E = (D*C)/(D+CB)
... although I think a compass and straight edge solution is what is being sought

Posted by Larry
on 20101003 14:14:53 