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在几何问题中,常有一些题涉及到动点、动直线或动圆,并求证与之相关的线段之间的和、差、积、商为定值,或证角与角之间的数量不变性,等等．这类问题通常是指平面几何中的定值问题．对于求定值、定点的问题,通常先用特殊条件(极端化)确定这个定值、定点,然后再来证明所得的结果．例1 (第18届加拿大数学奥林匹克试题)如图1, 定长的弦ST在一个以AB为直径的半圆周上滑动,M是 ST的中点,P是S对AB作垂线的垂足．求证:不管ST滑到什么位置, ∠SPM是一定角．
In geometric problems, there are often questions involving moving points, moving lines or moving circles, and verifying the sum, difference, product, and quotient between the line segments related to it, or the number of angles between the proof angle and the angle. Invariability, etc. This type of problem usually refers to the fixed-value problem in plane geometry. For the fixed value and fixed point problems, the fixed value and fixed point are usually determined by special conditions (extreme), and then the obtained results are proved. Example 1 (18th Canadian Mathematical Olympiad Question) As shown in Fig. 1, a fixed-length string ST slides on a semi-circle with AB as the diameter, M is the midpoint of ST, and P is the perpendicular foot of S to AB. . Proof: Regardless of where the ST slides, ∠SPM is a certain angle.