关于广州市番禺区2024九上数学期末考24的解析

题目描述

MN是圆O上的一条不经过圆心的弦，MN=4，在劣弧MN和优弧MN上分别有点A，B（不与M，N重合），且$\stackrel\frown{AB}$=$\stackrel\frown{BN}$，连接$AM$ ，$BM$．

（3）如图，连接$AN$，$BN$，试猜想$AM·MB+AN·NB$的值是否为定值，若是，请求出这个值.

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

讲解

$AM·MB+AN·NB$？熟不熟悉？是否想到托勒密定理？

是的，这就是类似托勒密的一种特殊情况。
记得托勒密怎么证的吗？就是做角等。
好家伙，题面上不就有角等吗？！！（$\stackrel\frown{AB}$ = $\stackrel\frown{BN}$）

思路清晰了吧。
连接$AB$交$MN$与H

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

$$\because \stackrel\frown{AB}=\stackrel\frown{BN}$$

$$\therefore \angle AMN=\angle NMB$$

$$\therefore \triangle MAN\sim \triangle MHB,\triangle MAN\sim \triangle AHN$$

$$\frac{AM}{MH}=\frac{MN}{BN},\frac{AN}{MN}=\frac{NH}{AN}$$

$$AM·BN=MN·MH,AN^{2}=MN·NH$$

$$AM·BN+AN·BN=AM·BN+AN^{2}=MN·MH+MN·NH=MN·(MH+NH)=MN·MN=MN^{2}=16$$

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

如图为第一组相似$\triangle MAN\sim \triangle MHB$

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

如图为第二组相似$\triangle MAN\sim \triangle AHN$