初二數(shù)學(xué)經(jīng)典難題

1、2012年初二數(shù)學(xué)經(jīng)典難題一、解答題（共10小題，滿分100分）1已知：如圖，p是正方形abcd內(nèi)點(diǎn)，pad=pda=15求證：pbc是正三角形（初二）2已知：如圖，在四邊形abcd中，ad=bc，m、n分別是ab、cd的中點(diǎn)，ad、bc的延長(zhǎng)線交mn于e、f求證：den=f3如圖，分別以abc的邊ac、bc為一邊，在abc外作正方形acde和cbfg，點(diǎn)p是ef的中點(diǎn)，求證：點(diǎn)p到ab的距離是ab的一半4設(shè)p是平行四邊形abcd內(nèi)部的一點(diǎn)，且pba=pda求證：pab=pcb5p為正方形abcd內(nèi)的一點(diǎn)，并且pa=a，pb=2a，pc=3a，求正方形的邊長(zhǎng)6一個(gè)圓柱形容器的容積為v立方米，開(kāi)

2、始用一根小水管向容器內(nèi)注水，水面高度達(dá)到容器高度一半后，改用一根口徑為小水管2倍的大水管注水向容器中注滿水的全過(guò)程共用時(shí)間t分求兩根水管各自注水的速度7如圖1，已知正比例函數(shù)和反比例函數(shù)的圖象都經(jīng)過(guò)點(diǎn)m（-2，-1），且p（-1，-2）為雙曲線上的一點(diǎn)，q為坐標(biāo)平面上一動(dòng)點(diǎn)，pa垂直于x軸，qb垂直于y軸，垂足分別是a、b（1）寫(xiě)出正比例函數(shù)和反比例函數(shù)的關(guān)系式；（2）當(dāng)點(diǎn)q在直線mo上運(yùn)動(dòng)時(shí)，直線mo上是否存在這樣的點(diǎn)q，使得obq與oap面積相等？如果存在，請(qǐng)求出點(diǎn)的坐標(biāo)，如果不存在，請(qǐng)說(shuō)明理由；（3）如圖2，當(dāng)點(diǎn)q在第一象限中的雙曲線上運(yùn)動(dòng)時(shí)，作以op、oq為鄰邊的平行四邊形opcq，求

3、平行四邊形opcq周長(zhǎng)的最小值8如圖，p是邊長(zhǎng)為1的正方形abcd對(duì)角線ac上一動(dòng)點(diǎn)（p與a、c不重合），點(diǎn)e在線段bc上，且pe=pb（1）求證：pe=pd；pepd；（2）設(shè)ap=x，pbe的面積為y求出y關(guān)于x的函數(shù)關(guān)系式，并寫(xiě)出x的取值范圍；當(dāng)x取何值時(shí)，y取得最大值，并求出這個(gè)最大值9如圖，直線y=k1x+b與反比例函數(shù)yk2x（x0）的圖象交于a（1，6），b（a，3）兩點(diǎn)（1）求k1、k2的值（2）直接寫(xiě)出k1x+bk2x0時(shí)x的取值范圍；（3）如圖，等腰梯形obcd中，bcod，ob=cd，od邊在x軸上，過(guò)點(diǎn)c作ceod于點(diǎn)e，ce和反比例函數(shù)的圖象交于點(diǎn)p，當(dāng)梯形obcd的

4、面積為12時(shí)，請(qǐng)判斷pc和pe的大小關(guān)系，并說(shuō)明理由10如圖，已知直線y=12x與雙曲線ykx(k0)交于a，b兩點(diǎn)，且點(diǎn)a的橫坐標(biāo)為4（1）求k的值；（2）若雙曲線ykx(k0)上一點(diǎn)c的縱坐標(biāo)為8，求aoc的面積；（3）過(guò)原點(diǎn)o的另一條直線l交雙曲線ykx(k0)于p，q兩點(diǎn)（p點(diǎn)在第一象限），若由點(diǎn)a，b，p，q為頂點(diǎn)組成的四邊形面積為24，求點(diǎn)p的坐標(biāo)c29c91afe4ced1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afedd1b6c87d1b6c8795ad9c91afe4c

5、ed1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af95ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9d1b6c8795ad9c91afe4ced1b6c8795a1afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87

6、95ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c

7、8795ad29c91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91a

8、fe4ced1b6c8d1b6c8795ad9c91afe4ced1d91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c871afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795a

9、d9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6c8795ad9c91afe4ced1

10、b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8791afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afc91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91af

11、e4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c879

12、5ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad9c91afe4ced15ad9c91d1b6c8795ad9c91afe4ced1b

13、6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8795ad9c91afe4ced195ad9c91afe4ced1b6c8795ad91afe4ced1b6cd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6

14、c8795ad29c91af8795ad9c91fe4ced1d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c87d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af5d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afad9c91fe4ced1b6c8795ad29c91afb6c8795ad29c91afb6c8795ad29c91afd1b6

15、c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91affe4ced1b6c8795ad29c91afc8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad9c91afed1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8d1b6c8

16、795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af795ad9c91fe4ced1b6c8795add1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af29c91af4ced1b6c8795ad1b6c8795ad9c91afe4ced1b6c8795ad91afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795

17、ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afd1b6c8795ad29c91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afd91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c9d1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91af1afd1b6c8795ad9c91afe4ced1b6c8795ad91afe4ced1b6c8795ad9c91fe4ced1b6c8795ad29c91afd1bd1b6c