MathDB
Prove or disprove that

Source:

January 10, 2015
geometrygeometry proposed

Problem Statement

The quadrilateral ABCDABCD has an incircle of diameter dd which touches BCBC at KK and touches DADA at LL. Is it always true that the harmonic mean of ABAB and CDCD is equal to KLKL if and only if the geometric mean of ABAB and CDCD is equal to dd?
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