The document discusses properties of arcs, tangents, cyclic quadrilaterals, and chords in circles. It states that the angle at the center of a circle is twice the size of the angle at the circumference on the same arc. For tangents, the angle between the tangent and radius is 90 degrees, and two tangents drawn from an external point are equal. Opposite angles of a cyclic quadrilateral are supplementary, and exterior angles equal interior opposite angles. Properties of chords include equal chords being equal distance from the center and perpendicular bisectors of chords passing through the center.

1. PROPERTIES

15. Arc
• The angle at the centre is twice the size of angle on the circumference
• Angles on the circumference standing on the same arc are equal
• The angle in a semi-circle is a right angle
Tangent
o The angle between a tangent and the radius drawn to the point of contact is 90o
o From any external points, two equal tangents can be drawn
o An angle formed by a tangent with a chord drawn to the point of contact is equal to the
angle in the alternate segment
Cyclic Quadrilateral
 The opposite angles of a cyclic quadrilateral are supplementary
 The exterior angles of a cyclic quadrilateral is equal to its interior opposite angles
Chord
 Equal chords are equal distance from the center
 Perpendicular bisector of a chord passes through the center of the circle
 Equal chords subtend equal angles at the centre
 When two circles intersect, the segment joining their centers bisects the common chord at
right angles
 The products of the intercepts of intersecting chords are equal