On a semicircle with unit radius four consecutive chords
![AB,BC, CD,DE](/media/m/5/3/8/5384e36bea9295c071ea97c8c3d4fb54.png)
with lengths
![a, b, c, d](/media/m/a/b/a/aba147d136d904768670353792ec9289.png)
, 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
$$a^2 + b^2 + c^2 + d^2 + abc + bcd < 4.$$