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Question

Let A0,A1,A2,A3,A4,A5 be a regular hexagon inscribed in a unit circle with centre at the origin. Then the product of the lengths of the line segments A0A1,A0A2,A0A4 is


Your Answer
A
Your Answer
B
Correct Answer
C
Your Answer
D

Solution

The correct option is B

Let O be the centre of the circle of unit radius and the coordinates of A0 be (1,0)
Since each side of the regular hexagon makes an angle of 60 at the centre O.
Coordinates of A1 are (cos60,sin60)=(12,32)
A2 are (cos120,sin120)=(12,32)
A3 are (1,0)
A4 are (12,32) and A5 are (12,32)
Now A0A1=(112)2+(32)2=14+34=1
A0A2=(1+12)2+(32)2=94+34=3=A0A4
So that (A0A1) (A0A2) (A0A4)=3



 

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