Let A0A1A2A3A4A5  be a regular hexagon inscribed in a unit circle with centre at the origin. Then the product of the lengths of the line segments A0 A1, A0  A2    and A0  A4  is

Let O  be the centre of the circle of the unit radius and the coordinates of A0 be (1, 0). Since each side of the regular hexagon makes an angle of 600 at the centre O .Coordinates of A1 are (cos600, sin600)=(1/2,  3/2) A2  are (cos1200, sin1200)=(−1/2,  3/2) A3  are (−1,  0) A4  are (−1/2,  −3/2)  and A5  are (1/2, −3/2) Now A0A1=(1−12)2+(32)2=14+34=1 A0A2=(1+12)2+(32)2=94+34=3=A0A4 So that (A0A1)(A0A1)(A0A4)=3