The angle formed between a tangent and a chord is equal to the angle in the alternate segment of the circle.

When a tangent touches a circle at a specific point and a chord is drawn from that point, the angle between the tangent and the chord is referred to as the angle between the tangent and the chord. This angle is equal to the angle located in the alternate segment of the circle. The alternate segment is defined as the area of the circle that lies opposite to the angle formed by the chord inside the circle.

To illustrate this concept, consider a circle with a tangent that touches it at point $A$. If you draw a chord $AB$ from point $A$ to another point $B$ on the circumference of the circle, the angle between the tangent at point $A$ and the chord $AB$ is equal to the angle in the alternate segment. This alternate angle is subtended by the chord $AB$ at the circumference of the circle, specifically on the side opposite the chord.

This relationship is a consequence of the Alternate Segment Theorem, which states that the angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment. This theorem is invaluable for solving various problems related to circles, particularly those involving angles and tangents. By remembering this relationship, you can effectively analyze and solve circle geometry problems, which will be beneficial for your GCSE Mathematics examinations.