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Since, ABCDEF is a regular hexagon, all the sides are equal. The lines joining the center to the vertices OA, OB, OC, .. OF divide the angle at O in equal proportions.   Hence  angle 360 deg. is divided in to 6 equal parts.

Hence AOB, AOF, BOC, COD, DOE, EOF  each  = 360/6 = 60 deg

In the triangle OAB,  OA = OB, as they are equal to radius of circle.  Hence OAB is an isosceles triangle.   Hence      OBA = OAB .

        OAB = (180 - AOB )/2 = 60 deg

Hence all angles in OAB are equal. Hence it is an equilatera l  triangle.  Hence AB = radius of circle.

In other triangles also,  you can prove in a similar way, OBC= OCB and BC = radius.  and so on.   Hence, all sides are equal to the radius of the circle.

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