The document discusses properties of circles and angles related to circles. It defines the diameter as the axis of symmetry and explains that a radius perpendicular to a chord divides it into two equal parts. It also states that angles subtended by the same or equal length arcs are equal both at the circumference and at the center, and that the angle at the center is twice the angle at the circumference for the same arc. Additionally, it says that for a cyclic quadrilateral, opposite angles are supplementary and an exterior angle equals the interior opposite angle.

1. Chapter 3
Circles II

2. The diameter of a circle is the axis of symmetry of the circle.
A radius that is perpendicular to a chord divides the chord into two equal parts and vice-versa
Angles subtended at the circumference by the same arc or arcs of same length are equal

3. Angles subtended at the centre by arcs of same length are equal.
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Angle at the centre of a circle is twice the angle subtended at the circumference by the same arc.

4. Opposite angles of a cyclic quadrilateral are supplementary.
A + C = 180⁰
B + D = 180⁰
The exterior angle of a cyclic quadrilateral is equal to its interior opposite angle.
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