Geometry #1 - Angle Properties of Circles

Property 1: The Central angle or the angle subtended at the centre of a circle by an arc (or a chord) is twice that of the Inscribed angle or the angle subtended by the arc (or the chord) on any point of the remaining part of the circle.
Property 2: The Inscribed angle due to a chord through the center of the circle is 90^0.
Property 3: The Inscribed angles subtended by the same arc (or the same chord) are equal.
Property 4: The sum of the opposite angles of a cyclic quadrilateral is equal to 1800.