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<C wanted, AE + BD = AB, angle bisectors

Source: 2005 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p4

April 28, 2021

geometryanglesangle bisectorUkraine Correspondence

Problem Statement

The bisectors of the angles

A

and

B

of the triangle

ABC

intersect the sides

BC

and

AC

at points

D

and

E

. It is known that

AE + BD = AB

. Find the angle

\angle C