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 re: Construction by Charlie)

I have redrawn the diagram several times in ACAD with circles of various radii and the |BC| length also varying.

In some cases the angles at F and G appear to right angles.  When measured in fact I found cases where the angle was less than 90º
but in others it was actually greater.

Looked good too!

Posted by brianjn on 2010-10-04 21:13:39