Maths · Geometry and measures. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Circle theorems are fixed facts about angles and lengths in a circle. First learn the names of the parts: a chord joins two points on the circle, a tangent touches the circle at one point only, a sector is a slice cut by two radii, and a segment is the region between a chord and its arc.
In a question, look for what the diagram contains. A centre suggests the angle at the centre theorem. A diameter suggests a 90° angle. Four points on the circle suggest a cyclic quadrilateral. A tangent suggests a 90° angle with the radius or the alternate segment theorem.
Two radii always make an isosceles triangle, so its two base angles are equal. Many questions need this fact first.
Students often halve when they should double, or the other way round. The angle at the centre is the bigger one: it is twice the angle at the circumference, so check that your centre angle is larger.
Answer: Angle BCD = 104°
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