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DE passes through I, if <BAC = 60 ^o and BD = CE = BC

Source: 2021 All-Ukrainain Correspondence MO , grades 5-12 p7

June 24, 2022

geometrycollinearincenterequal segmentsUkraine Correspondence

Problem Statement

Let

I

be the center of a circle inscribed in triangle

ABC

, in which

\angle BAC = 60 ^o

and

AB \ne AC

. The points

D

and

E

were marked on the rays

BA

and

CA

so that

BD = CE = BC

. Prove that the line

DE

passes through the point

I