Problem

Source: Sharygin contest. The final raund. 2008. Grade 8. Second day. Problem 7

Tags: ratio, geometry unsolved, geometry



(F.Nilov) Given isosceles triangle $ ABC$ with base $ AC$ and $ \angle B = \alpha$. The arc $ AC$ constructed outside the triangle has angular measure equal to $ \beta$. Two lines passing through $ B$ divide the segment and the arc $ AC$ into three equal parts. Find the ratio $ \alpha / \beta$.