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Prove that $ID$ and $AC$ are parallel

Source: All-Russian Olympiad 1996, Grade 9, Second Day, Problem 6

April 18, 2013

geometrycircumcircleincentergeometry proposed

Problem Statement

In the isosceles triangle

ABC

(

AC = BC

) point

O

is the circumcenter,

I

the incenter, and

D

lies on

BC

so that lines

OD

and

BI

are perpendicular. Prove that

ID

and

AC

are parallel.
M. Sonkin