What is the angle in a segment of a circle?

The angle in a segment of a circle is the angle subtended by the chord at the circumference.

In more detail, a segment of a circle is the region bounded by a chord and the corresponding arc. The angle in a segment is specifically the angle formed at the circumference of the circle by two points on the chord. This angle is also known as the "angle subtended by the chord at the circumference."

To understand this better, imagine a circle with a chord AB. The segment is the area enclosed by the chord AB and the arc connecting points A and B. If you pick any point C on the arc (but not on the chord), the angle ACB is the angle in the segment. This angle is always the same, no matter where point C is on the arc, due to the properties of circles.

This concept is crucial in circle theorems, which are a key part of GCSE Maths. One important theorem related to this is the "Angle in a Semicircle" theorem, which states that the angle in a semicircle is always a right angle (90 degrees). This is a special case where the chord is the diameter of the circle.

Understanding the angle in a segment helps in solving various problems related to circles, such as finding missing angles or proving that certain lines are parallel or perpendicular. It’s a fundamental concept that builds the foundation for more advanced geometric principles.