The angle at the centre is twice any angle at the circumference standing on the same arc.
\(\angle AOB=2\angle ACB\)
(\(\angle\) at centre \(=2\angle\) at circumference)

If \(AB\) is a diameter, the angle at the circumference is a right angle.
\(\angle ACB=90^\circ\)
(\(\angle\) in semicircle)

Angles standing on the same chord, on the same side of it, are equal.
\(\angle ACB=\angle ADB\)
(\(\angle\)s in the same segment)

Opposite angles of a cyclic quadrilateral are supplementary.
\(a+b=180^\circ\)
(\(\angle\)s in opposite segments)

A right angle at the circumference requires the chord to be a diameter. Check that condition before quoting the angle-in-a-semicircle theorem.

Property	Statement and reason	Diagram
Angle at the centre
Angle in a semicircle
Angles in the same segment
Angles in opposite segments

Angle Properties of Circles

Angle Properties of Circles

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