Cambridge IGCSE Mathematics · Syllabus 0580 · Geometry
Circle Theorems I
What is Circle Theorems I?
The angle properties of a circle required by Cambridge IGCSE Mathematics 0580. Core C4.7 requires the first two: an angle subtended by a diameter at the circumference is a right angle, and a tangent is perpendicular to the radius at the point of contact. Extended E4.7 requires those two and four more: the angle at the centre is twice the angle at the circumference when both stand on the same arc; angles at the circumference standing on the same arc or chord are equal; opposite angles of a cyclic quadrilateral sum to 180 degrees; and the angle between a tangent and a chord equals the angle in the alternate segment.
This definition is part of the Geometry chapter in Cambridge IGCSE Mathematics.