Designs like the figure below are typical of the simple forms, based on the square and circle, that pupils may profitably incorporate in any work in art design that they may be doing at the time they are studying the circle and the problems relating to perpendiculars and squares.
Among the applications of the problem to draw a tangent to a given circle is the case of the common tangents to two given circles. Some authors give this as a basal problem, although it is more commonly given as an exercise or a corollary. One of the most obvious applications of the idea is that relating to the transmission of circular motion by means of a band over two wheels,[75] A and B, as shown on [page 226].
The band may either not be crossed (the case of the two exterior tangents), or be crossed (the interior tangents), the latter allowing the wheels to turn in opposite directions. In case the band is liable to change its length, on account of stretching or variation in heat or moisture, a third wheel, D, is used. We then have the case of tangents to three pairs of circles. Illustrations of this nature make the exercise on the drawing of common tangents to two circles assume an appearance of genuine reality that is of advantage to the work.
