Circle Theorems

 Circle Theorems

The Circle Theorems you need to be familiar with are as follows:

Angle at the Center Theorem:
The angle subtended at the center of a circle is twice the angle subtended at the circumference by the same arc.
Angle at the center = 2 * Angle at the circumference

Angle in a Semi-Circle Theorem:

The angle formed by any diameter of a circle in a semicircle is a right angle (90 degrees).

Angles in the Same Segment Theorem:

Angles in the same segment are equal.
Angles subtended by the same arc at the circumference are equal.

Opposite Angles in a Cyclic Quadrilateral:

The opposite angles of a cyclic quadrilateral (a quadrilateral whose vertices lie on a circle) are supplementary (add up to 180 degrees).

Tangent and Radius Theorem:

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Alternate Segment Theorem:

The angle between a tangent and a chord, drawn from the point of contact, is equal to the angle in the alternate segment.

Chord Properties:

• The perpendicular bisector of a chord passes through the center of the circle.
• Equal chords of a circle subtend equal angles at the center.
• In a circle, if two chords are equal in length, then they are equidistant from the center.

These are the main circle theorems covered in IGCSE 0580 Mathematics. It's important to understand these theorems and be able to apply them to solve problems involving circles