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21 Nov 2022, 08:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
56% (02:25) correct
44%
(01:39)
wrong
based on 41
sessions
History
Date
Time
Result
Not Attempted Yet
A hexagon with sides of equal length and interior angles of equal measure is inscribed in a circle. If the perimeter of the hexagon is 12, what is the perimeter of an equilateral triangle inscribed in the same circle?
A. 6
B. 9
C. 2√3
D. 3√3
E. 6√3
A. 6
B. 9
C. 2√3
D. 3√3
E. 6√3
21 Nov 2022, 12:55
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As the hexagon has same length of the sides and same internal angle, its a regular hexagon.
Hence the hexagon can be viewed as 6 equilateral triangles with side length of 2 cms (12/6).
Hence the radius of the circle is 2 cms.
Once the radius is known, we can find the length of the sides of the inscribed equilateral triangle.
Measure of each side of the triangle = \(\sqrt{3}\) * radius of the circle
Perimeter = 3 * Side Length = 3 * 2 * \(\sqrt{3}\) = \(6\sqrt{3}\)
The working is shown in the attached image.
IMO E
Hence the hexagon can be viewed as 6 equilateral triangles with side length of 2 cms (12/6).
Hence the radius of the circle is 2 cms.
Once the radius is known, we can find the length of the sides of the inscribed equilateral triangle.
Measure of each side of the triangle = \(\sqrt{3}\) * radius of the circle
Perimeter = 3 * Side Length = 3 * 2 * \(\sqrt{3}\) = \(6\sqrt{3}\)
The working is shown in the attached image.
IMO E
Attachments
Screenshot 2022-11-22 012024.png [ 147.14 KiB | Viewed 5534 times ]
20 Apr 2025, 13:43
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