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Nội dung: <blockquote data-quote="kt1996" data-source="post: 151655" data-attributes="member: 299144">(xin lỗi vì mình không vẽ hình đc:stupid<img src="https://cdn.jsdelivr.net/gh/twitter/twemoji@14.0.2/assets/72x72/1f642.png" class="smilie smilie--emoji" loading="lazy" width="72" height="72" alt=":)" title="Smile    :)"  data-smilie="1"data-shortname=":)" />Gọi I,K lần lượt là tâm đ tròn đk HB, HC  nối  các đoạn thẳng IE, HE,HF,KF, EF, AH*Xét <img src="https://codecogs.izyba.com/png.latex?\triangle BIE và \triangle HIE" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> ta có: <img src="https://codecogs.izyba.com/png.latex?\widehat{IBE} =\widehat{IEB}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (vì <img src="https://codecogs.izyba.com/png.latex?\triangle BIE" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> cân tại I) <img src="https://codecogs.izyba.com/png.latex?\widehat{IHE} =\widehat{IEH}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (vì <img src="https://codecogs.izyba.com/png.latex?\triangle HIE" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> cân tại I)Trong <img src="https://codecogs.izyba.com/png.latex?\triangle BHE" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> ta có:<img src="https://codecogs.izyba.com/png.latex?\widehat{IBE}+\widehat{IEB}+\widehat{IHE}+\widehat{IEH}=180^{o}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Từ trên => <img src="https://codecogs.izyba.com/png.latex?\widehat{IEB}+\widehat{IEH}=90^{o}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />hay <img src="https://codecogs.izyba.com/png.latex?HE \perp AB" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?(1)" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />*Tương tự đối với cặp <img src="https://codecogs.izyba.com/png.latex?\triangle HKF và \triangle CKF" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> ta được: <img src="https://codecogs.izyba.com/png.latex?HF \perp AC" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?(2)" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Từ (1), (2) => Tứ giác AEHF là hcn*Xét <img src="https://codecogs.izyba.com/png.latex?\triangle AFE và \triangle ABC" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> ta có:<img src="https://codecogs.izyba.com/png.latex?\widehat{A}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> chung <img src="https://codecogs.izyba.com/png.latex?(3)" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="https://codecogs.izyba.com/png.latex?\widehat{AFE}=\widehat{AHE}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> (dễ nhận thấy)ta lại có:<img src="https://codecogs.izyba.com/png.latex?\widehat{AHE}+\widehat{IHE}=90^{o}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />mà  <img src="https://codecogs.izyba.com/png.latex?\widehat{IHE}+\widehat{IBE}=90^{o}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />=><img src="https://codecogs.izyba.com/png.latex?\widehat{AFE}=\widehat{IBE}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> <img src="https://codecogs.izyba.com/png.latex?(4)" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />Từ (3), (4) => <img src="https://codecogs.izyba.com/png.latex?\triangle AFE" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /> đồng dạng với <img src="https://codecogs.izyba.com/png.latex?\triangle ABC" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />=><img src="https://codecogs.izyba.com/png.latex?\frac{AE}{AC}=\frac{AF}{AB}" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />hay AE.AB =AF.AC (đpcm)</blockquote>

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