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2 angle bisectors concurrent with a line, AD = DE, BC = EC

Source: Mathematics Regional Olympiad of Mexico West 2016 P4

September 7, 2022

geometryconcurrencyconcurrent

Problem Statement

Points

A, B, C

and

D

lie on a circle, in that order clockwise, such that there is a point

E

on segment

CD

with the property that

AD = DE

and

BC = EC

. Prove that the intersection point of the bisectors of the angles

\angle DAB

and

\angle ABC

is on the line

CD