SOLUTION: ABC is an equilateral triangle with circumcentre O. What is the ratio AO+BO+CO to the perimeter of the triangle?

Question 1102503: ABC is an equilateral triangle with circumcentre O. What is the ratio AO+BO+CO to the perimeter of the triangle?
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

AO, BO, and CO divide the equilateral triangle into three isosceles triangles, each with an angle measuring 120 degrees. Each of those triangles can be divided into two 30-60-90 right triangles.

The geometry of 30-60-90 right triangles tells us that the ratio of AO to the side of the triangle is 1:sqrt(3).

Therefore the ratio of AO+BO+CO to the perimeter of the equilateral triangle is 1:sqrt(3).
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