MathDB

ASU 058 All Russian MO 1965 line passes through incenter

Source:

June 19, 2019

geometryincenterCircumcenter

Problem Statement

A circle is circumscribed around the triangle

ABC

. Chords, from the midpoint of the arc

AC

to the midpoints of the arcs

AB

and

BC

, intersect sides

[AB]

and

[BC]

in the points

D

and

E

. Prove that

(DE)

is parallel to

(AC)

and passes through the centre of the inscribed circle.