arthuro69 wrote:
What is the perimeter of an equilateral triangle inscribed in a circle of radius 4 ?
A. \(6\sqrt{2}\)
B. \(6\sqrt{3}\)
C. \(12\sqrt{2}\)
D. \(12\sqrt{3}\)
E. \(24\)
So, here's what the diagram looks like.
If we draw lines from the center to each vertex, we get the following:
Since the radii have length 4, we can add that here:
Now we'll draw a line from the center that is PERPENDICULAR to one side of the tirangle.
We now have a SPECIAL 30-60-90 right triangle.
Here's the base version of this SPECIAL TRIANGLE
We can see that the each 30-60-90 triangle in the diagram is TWICE as big as the base version. So, each side opposite the 60º angle must have length 2√3
This means ONE side of the equilateral triangle has length 4√3, so the PERIMETER = 4√3 + 4√3 + 4√3 = 12√3
Answer: C
Cheers,
Brent
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