2/28/2023 0 Comments Octagon angle![]() ![]() These relationships can be discovered using the right triangle, with sides: the circumradius, the inradius and half the octagon edge, which is shown in the next figure. The radius of circumcircle, R_c, and incircle, R_i, are related to the length of the edges, \alpha. Circumscribed and inscribed circles of regular octagon The incircle is tangent to all eight edges and its center is the same with that of the circumcircle. The radius of incircle R_i is usually called inradius. This circle is called inscribed circle or incircle. The radius of circumcircle R_c is usually called circumradius.Īnother circle can also be drawn, that passes through the midpoints of the octagon edges. Likewise, the diagonals of the octagon are diameters of the circumcircle. This is the cirmuscribed circle or circumcircle. The center of this circle is the center of the octagon. Like any regular polygon, a circle can be drawn that passes through all eight vertices of the octagon. The regular octagon is composed by eight identical isosceles triangles having a common vertex, the polygon centre. Half of them pass through diagonally opposite vertices and the remaining ones, pass through the midpoints of opposite edges. The regular octagon features eight axes of symmetry. The diagonals of an octagon separate its interior into 6 triangles Properties of regular octagons Symmetry Since the sum of internal angles in one triangle is 180°, it is concluded that 6 triangles, side by side, should measure up to 6x180=1080°. The vertices can be connected in different ways (resulting in different triangles), however the number of triangles remains constantly six. This way, exactly six triangles can be defined inside the octagon. To do so, we have to connect all vertices through straight lines, avoiding any intersections. This can be easily be concluded by finding out how many triangles can be fitted inside the octagon. The sum of the internal angles of any octagon, either convex or concave is always 1080°. Any octagon that is not regular is called irregular. As demonstrated in the figure below, many possible concave octagons can be defined, with equal sides, but unequal interior angles. Having only the sides equal is not adequate, in that matter, since the octagon may be concave, with equal sides. An octagon is called regular when its sides are equal and also its interior angles are equal. ![]() To the contrary, a concave octagon (or polygon) has one or more of its interior angles greater than 180°. A convex octagon has none of its interior angles greater than 180°. ![]() An octagon, like any other polygon, can be either convex or concave, as illustrated in the next figure. Octagon is a polygon with eight sides and eight vertices. ![]()
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