How do you find the angle subtended by a chord at the circumference?

To find the angle subtended by a chord at the circumference, use the circle theorems involving angles and chords.

In more detail, the angle subtended by a chord at the circumference of a circle can be found using the circle theorems. One key theorem states that the angle subtended by a chord at the circumference is equal to the angle subtended by the same chord at any other point on the circumference, provided both angles are on the same side of the chord. This is known as the "Angle at the Centre Theorem."

To apply this theorem, first identify the chord and the points on the circumference where the angles are subtended. If you know the angle subtended by the chord at the centre of the circle, you can use the fact that the angle at the centre is twice the angle at the circumference. For example, if the angle at the centre is 80 degrees, the angle subtended by the chord at the circumference would be 40 degrees.

Another useful theorem is the "Alternate Segment Theorem," which states that the angle between a chord and a tangent through one of the endpoints of the chord is equal to the angle in the alternate segment. This can help in situations where a tangent is involved.

By understanding and applying these theorems, you can accurately find the angle subtended by a chord at the circumference of a circle. Practising with different problems will help reinforce these concepts and improve your confidence in using them.