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 Construction by brianjn)

Constructing this with Geometers Sketchpad results in |EF| = |GE|, but angles A'FE and C'GE are each larger than 90 degrees and so those two segments do not lie on a tangent line and the distances are therefore not the tangential distance.

Posted by Charlie on 2010-10-04 12:05:22