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RMO 2015 Karnataka geometry, circumcenter lies on an angle bisector

Source: CRMO 2015 region 4 (Karnataka) p1

September 30, 2018
geometryCircumcenterincenterreflection

Problem Statement

Let ABCABC be a triangle. Let B′B' denote the reflection of bb in the internal angle bisector ll of ∠A\angle A.Show that the circumcentre of the triangle CB′ICB'I lies on the line ll where II is the incentre of ABCABC.
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