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lines intersect on circumcircle

Source: Moldova 2000 Grade 11 P8

April 27, 2021

geometrycircumcircle

Problem Statement

In an isosceles triangle

ABC

with

BC=AC

and

\angle B<60^\circ

,

DE

is the incenter and

O

the circumcenter. The circle with center

E

that passes through

A,O

and

I

intersects the circumcircle of

\triangle ABC

again at point

D

. Prove that the lines

DE

and

CO

intersect on the circumcircle of

ABC

.

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