an equilateral triangle is inscribed in a circle of radius r. expresss the circumference C as function of the?

Question

length x , side of the triangle
answer is 2 pix / SR 3 .pls explain

SR: square root

Answer 1

-to have an equilateral triangle each and each perspective has to equivalent 60 -the line r bisects the attitude from the centroid of the triangle so all of us know the two sides of that r has an perspective equivalent to 30 -drawing a line quickly down from the middle of the triangle you create yet another triangle that consists of r as one side and 4d5e329de03f39dcdac4a425810f9be4d5e329de03f39dcdac4a425810f9be4d5e329de03f39dcdac4a425810f9be of (a million/2)x as yet another side and that's a ninety degree triangle so understanding that the attitude is 30 you should use trig to unravel something and create a formula -like so: cos30 = [4d5e329de03f39dcdac4a425810f9be4d5e329de03f39dcdac4a425810f9be4d5e329de03f39dcdac4a425810f9be4d5e329de03f39dcdac4a425810f9be4d5e329de03f39dcdac4a425810f9be4d5e329de03f39dcdac4a425810f9be] (a million/2)x r so now you isolate the radius and as quickly as you isolate the radius you know that the circumerence = pi (a million/2)x dia = pi (a million/2)x 4d5e329de03f39dcdac4a425810f9ber plug on your equation you got here up with into the r value for the circumference and thats your answer

Answer 2

Best way to solve problems like this is to draw a little sketch and see how things are related. If you drop a line from a vertex to the midpoint of the opposite side you make a right triangle where you know the hypothenuse and the base. You also have a slimilar triangle with the base from the center of the circle to a side. You can get what you need from these. Draw the sketch!

Answer 3

draw the figure and put a radius to an angle of the triangle
draw a line segment down from the center so that it bisects a side of the triangle perpendicularly
now we have a right triangle with hypoteneuse "r" and one leg is x/2
this triangle is a 30-60-90 since the original triangle was equilateral
the other leg is then x/(2Sqrt[3])
solving for r in terms of x we get r=x/Sqrt[3]
C=2Pir= 2Pix/Sqrt[3]