Congruent incircles can be obtained by drawing a cevian in a triangle that divides it into two triangles having incircles of equal size. The positions and sizes of these two incircles can then be determined by simultaneously solving the eight equations
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(1)
|
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(2)
|
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(3)
|
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(4)
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(5)
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(6)
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(7)
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(8)
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for the eight variables 
, 
, 
, 
, 
, 
, 
, and 
, with 
, 
, and 
given. Generalizing to 
congruent circles gives the 
equations
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(9)
|
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(10)
|
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(11)
|
for 
,
..., 
,
 |
(12)
|
for 
,
..., 
,
and
 |
(13)
|
to be solved for the unknowns 
and 
(
of them), 
and 
(
of each for 
, ..., 
), and 
, 
, 
, and 
, a total of 
unknowns.
Given an arbitrary triangle, let 
Cevians be drawn from one of its vertices so all of the
triangles so determined have equal incircles. The equal
incircles theorem says that the incircles determined by spanning 2, 3, ..., 
adjacent triangles are also equal
(Wells 1991, p. 67).
