This document discusses several theorems related to circles. It states that the angle at the center of a circle is twice the angle at the circumference. The angle between a tangent and a chord is equal to the angle in the alternate segment. Opposite angles in a cyclic quadrilateral add up to 180 degrees. Tangents from a point are equal in length and the angle between a tangent and the radius is 90 degrees. The perpendicular line from the center of a circle to a chord bisects the chord. Angles in the same segment are equal and the angle within a semicircle is 90 degrees.

1. Circles
Circle theorems
The angle at the centre
is twice the angle at
the circumference.
The angle between a tangent
and a chord is equal to the
angle in the alternate segment.
Opposite angles in a
cyclic quadrilateral
add up to 180°.
Tangents from a point
are equal in length.
The angle between a tangent
and the radius is 90°.
The perpendicular line from
the centre of a circle to a
chord bisects the chord.
Angles in the same segment
are equal.
The angle within a
semicircle is 90°.