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