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Projection of vertex onto bisectors

Source: ITAMO 2016, Problem 1

May 11, 2016

geometryangle bisectorprojection

Problem Statement

Let

ABC

be a triangle, and let

D

and

E

be the orthogonal projections of

A

onto the internal bisectors from

B

and

C

. Prove that

DE

is parallel to

BC

.

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