how to calculate the length of a side of an equilateral triangle with vertices on a circle of diameter 1 cm
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Step-by-step explanation:
The center of the circle is also the point where all three medians intersect. Medians cut each other in proportion 2:1. So, the entire median (and height) is 1.5cm. Now, consider half of the equilateral triangle. Its sides are x, x/2 and 1.5, where x is the side of the equilateral triangle. By the Pythagorean theorem we have
(x/2)^2+1.5^2 = x^2.
Find x, then multiply it by 0.5 and by 1.5.
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