Circle theorems

Name: Angle at the center

Statement:
The angle at the center is twice the angle at the circumference standing on the same arc.

Name: Angles in the same segment

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

Name: Angle in a semicircle

Statement:
The angle subtended by a diameter at the circumference is 90°.

Name: Cyclic quadrilateral

Statement:
Opposite angles in a cyclic quadrilateral add up to 180°.

Name: Exterior angle of cyclic quadrilateral

Statement:
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

Name: Radius and tangent

Statement:
A radius is perpendicular to the tangent at the point of contact.

Name: Alternate segment theorem

Statement:
The angle between a tangent and a chord is equal to the angle in the opposite segment.

Name: Equal tangents

Statement:
Tangents drawn from the same external point to a circle are equal in length.