Tangents of a Circle


Tangent properties

Given a circle, a line is said to be a tangent to the circle if the line intersects the circle at exactly one point i.e. it "touches" the circle.  In the following diagram, the lines through point A and B are tangents to the circle.
he following are the basic properties of tangents that you should know in your high school:
We will use the above properties in various Euclidean constructions that involve tangents. 

Tangent of a circle through a given point

Given a circle centered at O and points A and P such that A lies on the circle and P is outside of the circle. Construct the tangents to the circle through points A and P as shown in the applet below. Note: What can you say about the locus of the point that forms a right-angled triangle with O and P?