MathDB

058

Part of 1965 All Russian Mathematical Olympiad

Problems(1)

ASU 058 All Russian MO 1965 line passes through incenter

Source:

6/19/2019
A circle is circumscribed around the triangle ABCABC. Chords, from the midpoint of the arc ACAC to the midpoints of the arcs ABAB and BCBC, intersect sides [AB][AB] and [BC][BC] in the points DD and EE. Prove that (DE)(DE) is parallel to (AC)(AC) and passes through the centre of the inscribed circle.
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