Bunuel wrote:
If the side of the regular hexagon above is 2, what is the circumference of the inscribed circle?
A. 2∏√3
B. 3∏
C. 4∏/√3
D. 2∏/√3
E. ∏√3
Attachment:
The attachment T6150.png is no longer available
Refer the diagram which I mentioned below:
Now AC will be 1 because circle is touching the midpoints of the circle.
Then we get kite ACBO.
We have AC = 1 and CB = 1, now we need to find BO which is radius
from triplets we get 30:60:90 = 1:√3:2
Now CBO is right angled triangle, then we get BO as √3.
r = √3...circumference is 2∏r is 2∏√3.
IMO option A.
Attachments
Hexa.PNG [ 9.9 KiB | Viewed 1999 times ]