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Geometry inequality involving tangent to incircle

Source: Italy TST 1999

February 1, 2011

geometryinequalitiesgeometry proposed

Problem Statement

Let

D

and

E

be points on sides

AB

and

AC

respectively of a triangle

ABC

such that

DE

is parallel to

BC

and tangent to the incircle of

ABC

. Prove that

DE\le\frac{1}{8}(AB+BC+CA)

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