MathDB

6

Part of 2015 Kazakhstan National Olympiad

Problems(1)

Prove or disprove that

Source:

1/10/2015
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?
geometrygeometry proposed