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WOLFRAM|DEMONSTRATIONS PROJECT

Three Circles with Two Common Tangents

point D

labels

colinear centers

second common tangent

Let

ABC

be a triangle circumscribed by the circle

. Let

be a point on

; form the line

. Consider three other circles

, and

with the common tangent

, with

inscribed in the triangle

ABC

, and

and

tangent to both the segment

and

. Prove that

, and

have two common tangents.

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