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1996年天津市中考数学试卷第21题是一道非常灵活的几何证明题,题目是: 如图,已知:AB是⊙O的直径,BC切⊙O于B点,OC平行于弦AD。求证:DC是⊙O的切线。 该题求证直线与圆相切,在初三教材中,证明直线与圆相切的判定定理只有一个,即“经过半径的外端并且垂直于这条半径的直线是圆的切线,”所以;连结辅助线OD是判定切线的必要题设条件。
In 1996, the 21st item of the Tianjin Mathematical Examination Questionnaire was a very flexible geometrical proof. The title is: As shown in the figure, AB is the diameter of ⊙O, BC is ⊙O is at point B, and OC is parallel to the string AD. Proof: DC is the tangent of ⊙O. The verification of the line is tangent to the circle. In the third grade textbook, it was proved that there is only one decision theorem tangent to the circle, ie, “the line passing through the outer end of the radius and perpendicular to this radius is the tangent of the circle,” so; The connection aid line OD is a necessary condition for determining the tangent line.