(1) A straight line that has only one point in common with a circle is the tangent of the circle.
(2) The straight line whose distance to the center of the circle is equal to the radius of the circle is the tangent of the circle.
(3) Judgment theorem of tangent: The straight line passing through the outer end of the radius and perpendicular to this radius is the tangent of the circle.
Second, the practice of auxiliary lines: there are two common methods to prove that a straight line is the tangent of a circle:
(1) When a straight line and a circle have a common point, connect the center of the circle with this common point to get the radius, and then prove that the straight line is perpendicular to this radius, and record it as "a known point, even the radius is proved to be perpendicular." Applying the judgment theorem of tangent line.
(2) When the common point of a straight line and a circle is unclear, make a vertical line passing through the center of the circle, and then prove that the distance (d) from the center of the circle to the straight line is equal to the radius (r), and record it as "the point is unknown, make it vertical, and prove the radius". Apply tangent recognition method (2).
Third, knowledge point 2:
Tangent Theorem: The tangent of a circle is perpendicular to the radius of the tangent point.
Fourth, the practice of auxiliary lines:
When a circle has a tangent, it is often the vertical radius of the tangent connecting the center of the circle and the tangent point. Notice "Look at the tangent, connect the radius, and get the perpendicularity."
Verb (abbreviation of verb) Click on the test center of the senior high school entrance examination: The determination and nature of tangent is the key content in the senior high school entrance examination. The test questions are flexible and diverse, and there are many questions to fill in the blanks, select topics, draw questions and solve problems.