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light beam inside equilateral reflecting - All-Russian MO 1996 Regional (R4) 8.6

Source:

September 23, 2024
geometrycombinatoricscombinatorial geometryreflection

Problem Statement

Spot spotlight located at vertex BB of an equilateral triangle ABCABC, illuminates angle α\alpha. Find all such values of α\alpha, not exceeding 60o60^o, which at any position of the spotlight, when the illuminated corner is entirely located inside the angle ABCABC, from the illuminated and two unlit segments of side ACAC can be formed into a triangle.
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