Maths · Geometry. 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 facts about angles that are always true in a circle. In a question, first look for what the lines are: a diameter, a radius, a tangent, or four points on the circle.
Many of the angles stand on an arc. The angle that an arc makes at the centre is twice the angle it makes at any point on the rest of the circumference. From this, all angles on the same arc are equal, and the angle on a diameter is 90°.
A cyclic quadrilateral has all four corners on the circle. A tangent meets the radius at 90°. Two radii always make an isosceles triangle.
When the point on the circumference is on the minor arc, students halve the small angle at the centre. Use the reflex angle at the centre instead: for example 360° − 100° = 260°, and half of 260° is 130°.
Answer: 136°
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