Given a circle, a line is said to be a [b][color=#0000ff]tangent[/color][/b] 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.

[font=Helvetica Neue, Helvetica, Arial, sans-serif][color=#333333]he following are the basic properties of tangents that you should know in your high school:[/color][/font][br][br][list][*][math]\angle CAO=\angle CBO=90^\circ[/math][br][/*][*][math]\angle ACO=\angle BCO[/math][/*][*][math]\angle AOC=\angle BOC[/math][/*][*][math]AC=BC[/math][br][/*][/list][br]We will use the above properties in various Euclidean constructions that involve tangents. 

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.[br][br][b]Note[/b]: What can you say about the locus of the point that forms a right-angled triangle with O and P?