Trên cung nhỏ BC của đường tròn ngoại tiếp tam giác đều ABC lấy một điểm P tuỳ ý. Gọi Q là giao điểm của AP và BC. Chứng minh BC2= AP . AQ
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Vì PB=MP nên tam giác BMP cân
Mà \(\widehat{MPB}\)=\(\widehat{MPC}\)(cùng chắn cung AB = cung AC) =60o
=> tam giác BMP đều
Xét tam giác AMB và tam giác CPB, có: AB=BC, AM=BP, góc MAB = PCB ( cùng chắn cung BP)
=> tam giác AMB = tam giác CPB => AM=CP
=> AP= AM+MP=CP+BP
Bạn Trần Phương LInh làm sai ở chỗ xét hai tam giác
Xét tam giác AMB và tam giác CPB có
AB = BC (tam giác ABC đều )
\(\widehat{ABM}=\widehat{CBP}\) ( CÙNG + \(\widehat{MBC}=60^0\))
MB = BP ( tam giác BMP đều )
=) tam giác AMB = tam giác CPB ( c - g - c )
![](https://rs.olm.vn/images/avt/0.png?1311)
a,Ta có góc ABC =góc BAC=góc BCA=60•(ABC là Δ đều ) =>BPA=60•
Xét ΔBAQ và ΔBAP có
góc A chung
góc ABQ=góc BPA(60•)
=> ΔBAQ~ΔBPA(g.g)
=>BA/PA=AQ/AB
=>BA2=AP.AQ mà AB=BC
=>BC2=AP.AQ(đpcm )
b,trên đoạn PA lây điểm M sao cho PM=PB thì ta có Tam giác PMB là tam giác đều
vì góc ACB=60=PBM=>ABM=PBC
=> tam giác ABM = tam giác CBP(c.g.c)=> AM=PC
=>PB+PC==PM+AM=PA
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi BC tiếp xúc với (I), (I1), (I2) lần lượt tại D,M,N. AP cắt EF tại H và tiếp xúc với (I1),(I2) lần lượt tại Q,R.
Ta có \(EF=MN;EF=HE+HF=2HQ+QR;MN=PM+PN=2PR+RQ\)
Suy ra \(HE=PN\)
Lại có \(DN=PD+PN=CD-CP+PN=\frac{CA+BC-AB+CP+PA-CA-2CP}{2}\)
\(=\frac{BP+PA-AB}{2}=PM\) hay \(PN=DM\). Suy ra \(HE=DM\)
Mà tứ giác EFNM là hình thang cân nên \(HD||EM||FN\)
Nếu gọi DH cắt lại (I) tại K thì các tam giác cân \(EI_1M,KID,FI_2N\) đồng dạng có các cạnh tương ứng song song đôi một
Do đó \(II_1,DM,KE\) đồng quy tại B, \(II_2,DN,KF\) đồng quy tại C
Nói cách khác, BE và CF cắt nhau tại K. Vậy BE và CF gặp nhau trên (I).
![](https://rs.olm.vn/images/avt/0.png?1311)
góc APB=góc AQB=1/2*180=90 độ
=>AQ vuông góc BC, BP vuông góc CA
góc CPH+góc CQH=180 độ
=>CPHQ nội tiếp
Lời giải:
$\widehat{APB}=\widehat{ACB}=60^0$ (góc nt cùng nhìn cung $AB$)
$\widehat{ABC}=60^0$
$\Rightarrow \widehat{APB}=\widehat{ABC}=\widehat{ABQ}$
Xét tam giác $APB$ và $ABQ$ có:
$\widehat{APB}=\widehat{ABQ}$
$\widehat{A}$ chung
$\Rightarrow \triangle APB\sim \triangle ABQ$ (g.g)
$\Rightarrow \frac{AP}{AB}=\frac{AB}{AQ}\Rightarrow AB^2=AP.AQ$
Mà $AB=BC$ nên $BC^2=AP.AQ$ (đpcm)
Hình vẽ:
![](data:image/png;base64,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)