Join E the centre of the circle D.
Bisect D E in F. With F as centre and F E radius describe the circle D B E cutting the given circle in A and B. Draw the required tangents from D to touch the given circle at A and B. N.B.—A tangent to a circle or arc is always at right angles to a radius drawn to the point of contact.
Fig. 9
[Fig. 15] To draw an Exterior Tangent to two given circles A B and C D K.
Join the centres E and F cutting the circumference of the larger circle at K. Bisect E F in G. From K in the line K F cut off a part K P equal to the radius of the smaller circle E B.
With centre G and radius K F describe a semicircle; with F as centre and radius F P describe a circle. The semicircle cuts this circle at H. Join F H, and produce it to C. At E draw E A parallel to F C. Join A C, which is the exterior tangent required.
[Fig. 16] To draw an Interior Tangent to two given circles B E and F D.