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4

Part of 2015 Regional Competition For Advanced Students

Problems(1)

Problem 4 -- Problematic Parallel and Perpendicular Proofs

Source: 46th Austrian Mathematical Olympiad Regional Competition Problem 4

7/14/2018
Let ABCABC be an isosceles triangle with AC=BCAC = BC and ∠ACB<60∘\angle ACB < 60^\circ. We denote the incenter and circumcenter by II and OO, respectively. The circumcircle of triangle BIOBIO intersects the leg BCBC also at point D≠BD \ne B.
(a) Prove that the lines ACAC and DIDI are parallel. (b) Prove that the lines ODOD and IBIB are mutually perpendicular.
(Walther Janous)
Austriageometry