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Given cut ratio of two angle bisectors

Source: Turkey TST 2002 - P2

April 6, 2013
ratiogeometryangle bisectorgeometry proposed

Problem Statement

In a triangle ABCABC, the angle bisector of ABC^\widehat{ABC} meets [AC][AC] at DD, and the angle bisector of BCA^\widehat{BCA} meets [AB][AB] at EE. Let XX be the intersection of the lines BDBD and CECE where ∣BX∣=3∣XD∣|BX|=\sqrt 3|XD| ve ∣XE∣=(3−1)∣XC∣|XE|=(\sqrt 3 - 1)|XC|. Find the angles of triangle ABCABC.
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