On a semicircle with unit radius four consecutive chords with lengths , respectively, are given. Prove that
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On a semicircle with unit radius four consecutive chords $AB,BC, CD,DE$ with lengths $a, b, c, d$, respectively, are given. Prove that
$$a^2 + b^2 + c^2 + d^2 + abc + bcd < 4.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1981
Školjka 
with lengths 
, respectively, are given. Prove that