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(2): Construction by brianjn)

Playing around with GSP it seems the greater the disparity between the sizes of the original circles, the smaller those angles are, and when the disparity is great enough, they are smaller than 90 degrees.

Posted by Charlie on 2010-10-05 01:05:46