Circle Theorems I

What is Circle Theorems I?

The six angle properties of a circle required by Cambridge O Level Mathematics: an angle subtended by a diameter at the circumference is a right angle; a tangent is perpendicular to the radius at the point of contact; 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 O Level Mathematics (Syllabus D).

Concepts related to Circle Theorems I

• subtended angle
• cyclic quadrilateral
• alternate segment