① Separation: A straight line and a circle have nothing in common.

② Tangency: A straight line and a circle have only one common point, which is called the tangent of the circle, and the only common point is called the tangent point.

③ Intersection: A straight line and a circle have two common points, which are called the intersection of the straight line and the circle, and the straight line is called the secant of the circle.

To judge the positional relationship between a straight line and a circle, let the radius ⊙O be R and the distance from the center of O to the straight line L be D. 。

(1) Does the straight line l intersect with ⊙O? dr。

Properties of tangents

The tangent of a circle is perpendicular to the radius passing through the tangent point.

② A straight line passing through the center and perpendicular to the tangent must pass through the tangent point.

The properties of tangents can be summarized as follows:

If a straight line satisfies any two of the following three conditions, then it must satisfy the third condition, namely:

① The straight line passes through the center of the circle;

② A straight line passes through the tangent point;

③ The straight line is perpendicular to the tangent of the circle.

Application of tangent property

According to the theorem, if the tangent of a circle appears, it is necessary to connect the radii of the tangent points, construct the theorem diagram and get the vertical relationship.

Judgement theorem of tangent: the straight line passing through the outer end of radius and perpendicular to the radius is the tangent of the circle.

Attention should be paid to when applying the judgment theorem:

① Tangent line must meet two conditions: a, passing through the outer end of radius; B, perpendicular to this radius, otherwise it is not the tangent of the circle.

② The tangent judgment theorem is actually derived from the conclusion that the straight line is tangent to the circle when the distance from the center of the circle to the straight line is equal to the radius.

(3) When judging that a straight line is tangent to a circle, it is often proved that the length of a line segment is equal to the radius by using the vertical segment with the center of the circle as the straight line without clearly pointing out whether the straight line and the circle have a common point in the known conditions, which can be simply said as "no intersection, making a vertical segment and proving the radius"; When it is clearly pointed out in the known conditions that there is a common point between a straight line and a circle, the radius of the common point is often connected, which proves that the radius is perpendicular to the straight line, which can be simply said as "there is an intersection point, making a radius, and proving verticality".