Theorems based on circles and tangents

Definition: A straight line which touches a circle at only one point is called a tangent to the circle and the point at which it touches the circle is called its point of contact.

• A tangent at any point on a circle is perpendicular to the radius through the point of contact.

• Only one tangent can be drawn at any point on a circle. However, from an exterior point of a circle two tangents can be drawn to the circle.

• The lengths of the two tangents drawn from an exterior point to a circle are equal.

• If two circles touch each other, then the point of contact of the circles lies on the line joining the centres.

• If two circles touch externally, the distance between theircentres is equal to the sum of their radii.

• If two circles touch internally, the distance between their centresis equal to the difference of their radii.