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Easy isosceles triangle geo

Source: Bulgarian Spring Tournament 2023 10.2

March 25, 2023
geometry

Problem Statement

An isosceles △ABC\triangle ABC has ∠BAC=∠ABC=72o\angle BAC =\angle ABC =72^{o}. The angle bisector ALAL meets the line through CC parallel to ABAB at DD.
a)a) Prove that the circumcenter of △ADC\triangle ADC lies on BDBD.
b)b) Prove that BEBL\frac {BE} {BL} is irrational.
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