The radius of the circle is 12 cm. Calculate the side of the regular hexagon inscribed in this circle.

Draw 6 radii from the center to the vertices of the hexagon. We get 6 congruent isosceles triangles (Lateral sides – radii, bases – sides of a regular hexagon) Angles formed by the center of the circle and adjacent radii are congruent (From the congruence of triangles) and form a circle => Sum of measures of these angles = 360 Measure of each angle = 360/6 = 60 We have: 6 congruent isosceles triangles, each has an angle of 60 => These triangles are equilateral => Hexagon side = radius = 12 cm.