Cho tam giác ABC vuông tại A, đường cao AH. Gọi E, F lần lượt là hình chiếu của H trên AB, AC
a, Cho AB=9, BH=5.4. Tính AC,BC,AH,EF ( đã làm được)
b, Chứng minh \(\dfrac{1}{EF^2}\)=\(\dfrac{1}{AB^2}\)+\(\dfrac{1}{AC^2}\)(đã làm được)
c, Chứng minh EA.EB+FA.FC=HB.HC( cần trợ giúp)
Lời giải:
Áp dụng hệ thức lượng trong tam giác vuông đối với tam giác vuông $AHB$, đường cao $HE$:
$EA.EB=HE^2$
Tương tự: $FA.FC=HF^2$
$\Rightarrow EA.EB+FA.FC=HE^2+HF^2=EF^2(1)$ (định lý Pitago)
Mặt khác: Dễ thấy $HEAF$ là hình chữ nhật do có 3 góc $\widehat{E}=\widehat{A}=\widehat{F}=90^0$
$\Rightarrow EF=HA$
$\Rightarrow EF^2=HA^2(2)$
Áp dụng hệ thức lượng trong tam giác vuông $ABC$:
$AH^2=HB.HC(3)$
Từ $(1);(2); (3)\Rightarrow EA.EB+FA.FC=HB.HC$ (đpcm)
Hình vẽ:
![](data:image/png;base64,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)