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angle bisectors -open problem?

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Otman

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Nov 10, 2017, 11:50:00 AM11/10/17
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equality of angles bisectors lengths in a triangle leads to an isosceles triangle is a well known theorem.
The only proofs are based on using the lengths formula of angle bisectors or proving by contradiction.a direct proof,surprisingly, is still challenging!.
Is a direct way to prove it( without the lengths formula) still unknown?
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