The perimeter of a regular triangle inscribed in a circle is 45 cm.Find the side of a regular

| August 12, 2021 | education

The perimeter of a regular triangle inscribed in a circle is 45 cm.Find the side of a regular octagon inscribed in the same circle

1. A triangle is called regular if all sides are equal.
The perimeter of a triangle with all sides equal is:
p = 3 / a, we express from this expression the side of the triangle:
a = p / 3 = 15 cm.
2. The radius of a circle circumscribed around a regular triangle is determined by the following expression:
R = a / √3 = 15 / √3 cm.
3. The radius of a circle circumscribed around a polygon is determined by the formula:
R = b / (2 / sin (180 / n)), where b is the side of the polygon, n is the number of corners.
Let us express b from this expression:
b = 2 * R * sin (180 / n)
In our case:
b = 2 * (15 / √3) * sin (180/8) = (30√3) * 0.382 = 6.62 cm.
Answer: side length 6.62 cm.



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