Tangents and Secants to a Circle — Formula Sheet

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Since there can be only one perpendicular OP at the point P, it follows that one and only one tangent can be drawn to a circle at a given point on the

Since there can be only one perpendicular to XY at the point P, it follows that the perpendicular to a tangent to a circle at its point of contact pas

No tangent can be drawn to a circle from a point inside the circle.

There is one and only one tangent to a circle at a point on the circle.

There are exactly two tangents to a circle through a point outside the circle.

The lengths of tangents drawn from an external point to a circle are equal.

OP^2 = OA^2 + PA^2

PA = PB

∠QAP = 2∠QPO = 2∠OQP

AB+CD=BC+DA

If two tangents AP and AQ are drawn to a circle with centre O from an external point A, then angle QAP = 2 angle QPO = 2 angle OQP.