Octagon eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° (formula_1 radians). The central angle is 45° (formula_2 radians). The area of a regular octagon of side length "a" is given by In terms of the circumradius "R", the area is In terms of the apothem "r" (see also inscribed figure), the area is These last two coefficients bracket the value of pi, the area of the unit circle. The area can also be expressed as where
Inscribed angle the case where the measure of the inscribed angle is the "difference" between two inscribed angles as discussed in the first part of this proof. Given a circle whose center is point "O", choose three points "V", "C", and "D" on the circle. Draw lines "VC" and "VD": angle "DVC" is an inscribed angle. Now draw line "VO" and extend it past point "O" so that it intersects the circle at point "E". Angle "DVC" subtends arc "DC" on the circle. Suppose this arc does not include point "E" within it. Point "E" is diametrically opposite to point "V". Angles