Tangent lines to circles

Tangent of a circle, each extending in the same plane line that exactly one point in common with the circle.

The running in the county level lines can be divided into secants, tangents and passers-by. The tangents put it in a certain way the limit is between secant and passers-by.

A basic property of the tangent is that it is at right angles to their contact radius, ie to the line connecting the contact point and the circle center. Conversely, any straight line that is perpendicular in the end point of a radius thereof, and a tangent of the circle. This is due to that the straight line at which the radius of a part (such as every straight line through the center of ) the axis of symmetry of the circle.

Construction of the tangent

For a construction with ruler and compass, it is sufficient not to find one by eye straight line that " just barely " touches the circle k.

• ( Or may be chosen arbitrarily ) If the contact point is given, then the first contact radius and then draw in the solder to the contact point.

• If a point P is given outside the circle through which the tangent should go, so first need to find the point of contact. Since this is a right angle must arise, helps the theorem of Thales: It connects the point P to the circle center point M and is characterized over the range [PM ] the Thales circle. This intersects the circle C at two points, which are useful as contact points. Therefore obtained by the point P two possible circle tangents. The by the two contact points called Straight certain polar of the point P with respect to the circle k

Analytic Geometry

Is a circle given the radius and the center by the equation

And is the point of contact,

So the equation of the tangent

Or

() Stands for any point on the tangent.