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side inequality in triangle

Source: LIMIT 2019 CAS1 P3

April 28, 2021
inequalitiesGeometric Inequalitiesgeometry

Problem Statement

In △ABC\triangle ABC, ∣AB‾∣=∣AC‾∣\left|\overline{AB}\right|=\left|\overline{AC}\right|, DD is the foot of the perpendicular from CC to ABAB and EE the foot of the perpendicular from BB to ACAC, then <spanclass=′latex−bold′>(A)</span> ∣BC‾∣3>∣BD‾∣3+∣BE‾∣3<span class='latex-bold'>(A)</span>~\left|\overline{BC}\right|^3>\left|\overline{BD}\right|^3+\left|\overline{BE}\right|^3 <spanclass=′latex−bold′>(B)</span> ∣BC‾∣3<∣BD‾∣3+∣BE‾∣3<span class='latex-bold'>(B)</span>~\left|\overline{BC}\right|^3<\left|\overline{BD}\right|^3+\left|\overline{BE}\right|^3 <spanclass=′latex−bold′>(C)</span> ∣BC‾∣3=∣BD‾∣3+∣BE‾∣3<span class='latex-bold'>(C)</span>~\left|\overline{BC}\right|^3=\left|\overline{BD}\right|^3+\left|\overline{BE}\right|^3 <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
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