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CD >DE if 2AD> AC+ AE

Source: 1989 Greece MO Grade X p3

September 7, 2024
geometrygeometric inequality

Problem Statement

From a point AA not on line ε\varepsilon, we drop the perpendicular ABAB on ε\varepsilon and three other not perpendicular lines ACAC, ADAD,AEAE which lie on the same semiplane defines by ABAB, such that (AD)>12((AC)+(AE))(AD )>\frac{1}{2}((AC)+(AE)). Prove that (CD)>(DE).(CD )>(DE). (Points B,C,D,,EB,C,D,,E lie on line ε\varepsilon ) .
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