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
This description may leave a little to be desired but I believe that it fulfils the requirements:
Let the centre of circle AB be A'.
Let the centre of circle CD be C'.
Construct square XYCB.
Join A' to X intersecting circle AC at F.
Join C' to Y intersecting circle CD at G.
Join F to G.
Construct a perpendicular bisector of FG to intersect line BC at E.
FE = GE.

Posted by brianjn
on 20101004 02:20:35 