Circles
 Secant: A line which intersects a circle at two distinct points is called a secant of a circle.
 Tangent: A line touching a circle at exactly one point only is called a tangent to the circle at that point.
 Point of contact: The point P at which the tangent touches the circle is called the point of contact.
 Number of tangents to a circle:
Position of the point w.r.t. the circle

Number of tangents

Inside

0

On

1

Outside

2

 Length of a tangent: The length of the line segment of the tangent between a given point and the given point of contact with the circle is called the length of the tangent from the point to the circle.
The tangent at any point of a circle is perpendicular to the radius through the point of contact. In other words, the angle between a tangent and the radius through the point of contact is\[{{90}^{o}}\].
 The lengths of tangents drawn from an external point to a circle are equal.
If AP and AQ are two tangents from an external point A to the circle, then AP = AQ.
 Two tangents drawn from an external point subtend equal angles at the centre and are equally inclined to the line segment joining the centre to that point.
 The tangents drawn at the ends of a diameter of a circle are parallel.
 The line segments joining the point of contact of two parallel tangents to a circle is a diameter of the circle.
 The angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the centre.
 There is one and only one tangent at any point on the circumference of a circle.
 A parallelogram circumscribing a circle is a rhombus.
 The opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
\[\angle AOB+\angle COD={{180}^{o}}\]
\[\angle BOC+\angle AOD={{180}^{o}}\]
 In two concentric circles, the chord of the larger circle which touches the smaller circle is bisected at the point of contact.
\[\text{AP}=\text{PB}\]
 If PAB is a secant to a circle intersecting it at A and B and PT is a tangent, then\[\text{PA}\times \text{PB}=\text{P}{{\text{T}}^{\text{2}}}\].