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4(BC + CA)< 5AB if 2 < BAC + 3 <ABC= 180^o

Source: I Soros Olympiad 1994-95 Ukraine R2 11.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 6, 2024
geometryanglesgeometric inequality

Problem Statement

It is known that in the triangle ABCABC, 2∠BAC+3∠ABC=180o 2 \angle BAC + 3 \angle ABC= 180^o. Prove that 4(BC+CA)<5AB4(BC + CA)< 5AB.
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