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|

(In reply to Does this work? by broll)

Once F and G are located, creating perpendiculars to O1F and O2G creates the respective tangent lines, and when this is done, it can be seen that these tangent lines don't meet on line AD. So any construction that leaves F and G where you found them and produces a point on line AD, is not producing the intersection of their tangent lines.

Posted by Charlie on 2010-10-04 12:16:49