Introduction:
A tangent is a line that touches a curve at a single point without crossing it. In the case of a circle, it is possible to demonstrate that there is one and only one tangent at any point on its circumference.

Proof:

1. Definition of a tangent:
A tangent to a circle is a line that intersects the circle at exactly one point, known as the point of tangency. The tangent is perpendicular to the radius drawn to the point of tangency.

2. Assume the existence of more than one tangent:
Let's assume that there are two tangents, AB and CD, at a point P on the circumference of the circle.

3. Drawing radii:
From the center of the circle, draw radii OP, OQ, OR, and OS towards the points of tangency A, B, C, and D, respectively.

4. Congruent triangles:
Since the radii are equal in length (all radii of a circle have the same length), we have:
OP = OQ and OR = OS.

5. Contradiction:
Consider triangle OPA and triangle OPB. These two triangles share side OP and side OA is congruent to side OB since both are radii of the same circle. Additionally, angle OPA is congruent to angle OPB because both are right angles (tangents are perpendicular to the radius).

By the Side-Angle-Side (SAS) congruence criterion, triangle OPA is congruent to triangle OPB.

6. Only one tangent:
Since triangle OPA is congruent to triangle OPB, it means that angle POA is congruent to angle POB. However, this contradicts the fact that AB is a straight line.

Thus, our assumption that there are two tangents is incorrect.

7. Conclusion:
Therefore, there can only be one tangent at any point on the circumference of a circle.