(1) Tangents and circles have only one common point;

(2) The distance between the tangent and the center of the circle is equal to the radius of the circle;

(3) The tangent line is perpendicular to the radius passing through the tangent point;

(4) The straight line whose center is perpendicular to the tangent must pass through the tangent point;

(5) The straight line perpendicular to the tangent passing through the tangent point must pass through the center of the circle;

(6) The tangent and secant of a circle are drawn from a point outside the circle, and the length of the tangent is the middle term in the length ratio of the two lines from this point to the intersection of the secant and the circle.

Where (1) is derived from the definition of tangent, (2) is derived from the position relation theorem of straight line and circle, and (6) is derived from similar triangles, that is, the tangent theorem.

decision

Judgment theorem of tangent:? Is the straight line passing through the outer end of the radius and perpendicular to this radius the tangent of the circle? . The tangent of a circle is perpendicular to the radius of the tangent point of the circle.

Geometric language: ∵l⊥OA, with point A on ⊙ O.

∴ The straight line L is tangent to⊙ O (tangent judgment theorem)

The property theorem of tangent:? The tangent of a circle is perpendicular to the radius passing through the tangent point.

Geometric language: ∵OA is the radius of ⊙O, and the straight line L cuts ⊙O at point A.

∴l？ ⊥OA (tangent property theorem)

Inference 1? The diameter passing through the center of the circle and perpendicular to the tangent must pass through the tangent point.

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