It's all on the circle

Geometry Level 2

Given that a,b,ca,b,c and dd are 4 distinct non-zero real numbers such that the points (a,1a)\left(a,\dfrac{1}{a}\right), (b,1b)\left(b,\dfrac{1}{b}\right), (c,1c)\left(c,\dfrac{1}{c}\right) and (d,1d)\left(d,\dfrac{1}{d}\right) lie on a circle.

Find the value of a×b×c×da\times b\times c\times d.

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