The angle ABC = 56^o as it is in the alternate segment to the angle CAE. Here, angle ABC is incorrectly calculated as 180 - 56 = 124^o. The angle is taken from 180^o which is a confusion with opposite angles in a cyclic quadrilateral. Opposite angles in a cyclic quadrilateral.Top tip: Use arrows to visualise which way the alternate segment angle appears: The chord BC is assumed to be parallel to the tangent and so the angle ABC is equal to the angle at the tangent. Parallel lines (alternate segment theorem).The angle at the circumference is assumed to be 90^o when the associated chord does not intersect the centre of the circle and so the diagram does not show a semicircle. They should total 90^o as the angle in a semicircle is 90^o. The angles that are either end of the diameter total 180^o as if the triangle were a cyclic quadrilateral. Look out for isosceles triangles and the angles in the same segment. Make sure that you know when two angles are equal. The angle at the centre is always larger than the angle at the circumference (this isn’t so obvious when the angle at the circumference is in the opposite segment). Make sure you know the other angle facts including:īy remembering the angle at the centre theorem incorrectly, the student will double the angle at the centre, or half the angle at the circumference.

Below are some of the common misconceptions for all of the circle theorems:

Ks3 area and perimeter worksheets