Suppose that A, B, C and D are four consecutive vertices of aregular polygon but do not assume that this polygon is inscribed ina circle. We know that there is some unique circle throughpoints A, B, C. Prove that this circle also goes throughD.
Hint: Let O be the center of the circle sothat OA=OB=OC. Use congruent triangles to show thatOC=OD.
Note: It follows easily from the result of thisexercise that every regular polygon can be inscribed in acircle.