Answer
The length of the tangent is directly proportional to the length of the corresponding arc. Therefore, if the arcs are congruent, then the tangents are congruent. Since the tangents all come together to form different sides, we obtain that the figure is a shape. In addition, since the angle formed by each side corresponds to the angle in the circle that it takes up, we see that the angles add to 360 degrees. Since the shape contains congruent sides and angles that add to 360 degrees, we find that the shape is a regular polygon.
