  In this paper, we present a novel method to draw a circle tangent to three
given circles lying on a plane. Using the analytic geometry and inversion
(reflection) theorems, the center and radius of the inversion circle are
obtained. Inside any one of the three given circles, a circle of the similar
radius and concentric with its own corresponding original circle is drawn.The
tangent circle to these three similar circles is obtained. Then the inverted
circles of the three similar circles and the tangent circle regarding an
obtainable point and a computable power of inversion (reflection) constant are
obtained. These circles (three inverted circles and an inverted tangent
circle)will be tangent together.Just,we obtain another reflection point and
power of inversion so that those three reflected circles (inversions of three
similar circles) can be reflections of three original circles, respectively. In
such a case,the reflected circle tangent to three reflected circles regarding
same new inversion system will be tangent to the three original ones. This
circle is our desirable circle. A drawing algorithm is also given for drawing
desirable circle by straightedge and compass. A survey of conformal mapping
theory and inversion in higher dimensions is also accomplished. Although,
Laguerre transformation might be used for solution of this problem, but we do
not make use of this method. Our novelty is just for drawing a circle tangent
to three given circles applying a tangent circle to three identical circles
concentric with three given ones and then inverting them as original ones by
compass and straightedge not any thing else.
