If A0,A1,A2,A3,A4 and A5 be a regular hexagon inscribed in a circle of unit radius. Then, the product of the lengths of the line segments A0A1,A0A2 and A0A4 is:
Now, (A0A1)2=(1−12)2+(0−√32)2=(12)2+(√32)2=14+34=1⇒A0A1=1(A0A2)2=(1+12)2+(0−√32)2=(32)2+(−√32)2=94+34=124=3⇒A0A2=√3 and (A0A4)2=(1+12)2+(0+√32)2=(32)2+(34)=94+34=124=3⇒A0A4=√3 Thus, (A0A1)(A0A2)(A0A4)=3