圆的切线是与圆密切关联的直线。在有关圆的问题中,常常出现圆的切线。解答时,若善于以切线为突破口,恰当运用有关圆的切线的几何定理,则能迅速找到解题途径。 一、运用切线的性质定理 例1 如图1,AB是⊙O的直径,P为AB延长线上一点,PD切⊙O于点C,BC和AD的延长线相交于点E,且AD⊥PD于D。(1)求证:AB=AE。(2)当AB:BP为何值时,△ABE为等边三 The tangent of a circle is a straight line that is closely related to the circle. In the question of circles, round tangents often appear. When answering, if you are good at taking the tangent line as the breakthrough, if you properly use the geometry theorem of the tangent of the circle, you can quickly find the way to solve the problem. First, the use of tangent properties Theorem Example 1 As shown in Figure 1, AB is the diameter of ⊙O, P is AB extension line, PD ⊙ O at point C, BC and AD extension line intersect at point E, and AD ⊥ PD to D. (1) Proof: AB=AE. (2) When AB:BP is the value, △ABE is equilateral three