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Regional Olympiad - FBH 2009 Grade 12 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2009

September 28, 2018
geometryEquilateral Trianglefixed

Problem Statement

Let ABCABC be an equilateral triangle such that length of its altitude is 11. Circle with center on the same side of line ABAB as point CC and radius 11 touches side ABAB. Circle rolls on the side ABAB. While the circle is rolling, it constantly intersects sides ACAC and BCBC. Prove that length of an arc of the circle, which lies inside the triangle, is constant
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