Regular Hexagon
STEPS:
Proof of Construction: PA = AB = BC = CD = DE since these lengths represent copies of the radius of circle O. But how do we know for sure that the last length, EP, coincided exactly with point P? Is EP actually the same length as the other copied radii? ΔDOE is an equilateral triangle since it has 3 sides of equal length (DO and OE are radii lengths and DE is a copy of this radii length). In similar fashion, ΔCOD, ΔBOC. ΔAOB and ΔPOA are also equilateral triangles. Since the interior angles of an equilateral triangle each contain 60º, m∠COD = m∠BOC = m∠AOB = m∠POA = m∠DOE = 60º. Since all of the central angles (surrounding a point) must add to 360º, we know the m∠POE = 60º (360º - 300º = 60º). Since we have ΔDOE ΔDOE by SAS. By CPCTC, and we know that the last copy of the radii coincides with point P making the hexagon truly inscribed. Hexagon PABCDE has all vertices on circle O, has congruent interior angles (each equal 120º) and has all sides congruent. PABCDE is an inscribed regular hexagon by definition.
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The re-posting of materials (in part or whole) from this site to the Internet is copyright violation 2. Which length should you set your compass to inscribe a regular hexagon in a circle? How do you find the length of a side of a hexagon inscribed in a circle?The short side of the right triangle is opposite the angle at the circle's center. So if we know the measure of the angle at the center, we can use the sine function to find the side length of the hexagon, since the radius is the hypotenuse: Thus, s = 2x = 2 (r sin θ).
What tools is used to inscribe a hexagon inside a circle?Sal constructs a regular hexagon that is inscribed inside a given circle using compass and straightedge.
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