As easy as a, b, c, d?

Geometry Level 3

If $\left(a,\dfrac{1}{a}\right),\left(b,\dfrac{1}{b}\right),\left(c,\dfrac{1}{c}\right)$ and $\left(d,\dfrac{1}{d}\right)$ are four distinct points on a circle of radius 4 units, then find the value of $abcd$ .