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|
Denote O1E by b and O2E by c
all the quantities on the right side are known:
r1-r2 difference of the radii
O1O2 distance between the circles' centers
BC =O1O2- (R1+R2)
b-c IS CONSTRUCTABLE (several ways , inter alia similar triangles or intersecting chords in a circle etc).
b-c and b+c define point E.
Very nice problem!!
Edited on October 3, 2010, 3:42 pm