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|BE - CE| < AD \sqrt3 when AB = BC= CD and AD \perp BC

Source: Czech-Polish-Slovak Junior Match 2015, Team p3 CPSJ

March 19, 2020
geometrygeometric inequalityequal segmentsperpendicular

Problem Statement

Different points AA and DD are on the same side of the line BCBC, with ∣AB∣=∣BC∣=∣CD∣|AB| = | BC|= |CD| and lines ADAD and BCBC are perpendicular. Let EE be the intersection point of lines ADAD and BCBC. Prove that ∣∣BE∣−∣CE∣∣<∣AD∣3||BE| - |CE|| < |AD| \sqrt3
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