gap gium cam on may bn nhiu

Tự kẻ hình nha !!

\(\frac{HA}{AA'}+\frac{HB}{BB'}+\frac{HC}{CC'}\)

\(=\frac{S_{HBC}}{S_{ABC}}+\frac{S_{AHB}}{S_{ABC}}+\frac{S_{AHC}}{S_{ABC}}\)

\(=\frac{S_{ABC}}{S_{ABC}}=1\)

uk thanks bn nhieu nha

Ta có:

\(\dfrac{HA'}{AA'}+\dfrac{HB'}{BB'}+\dfrac{HC'}{CC'}\)

\(\dfrac{HA'.BC}{AA'.BC}+\dfrac{HB'.AC}{BB'.AC}+\dfrac{HC'.AB}{CC'.AB}\)

\(\dfrac{S_{BHC}}{S_{ABC}}+\dfrac{S_{AHC}}{S_{ABC}}+\dfrac{S_{AHB}}{S_{ABC}}=\dfrac{S_{ABC}}{S_{ABC}}=1\)

Lời giải:

Ta thấy:

\(\left\{\begin{matrix} S_{HBC}=\frac{HA'.BC}{2}\\ S_{ABC}=\frac{AA'.BC}{2}\end{matrix}\right.\Rightarrow \frac{S_{HBC}}{S_{ABC}}=\frac{HA'}{AA'}(*)\)

\(\left\{\begin{matrix} S_{HAC}=\frac{HB'.AC}{2}\\ S_{ABC}=\frac{BB'.AC}{2}\end{matrix}\right.\Rightarrow \frac{S_{HAC}}{S_{ABC}}=\frac{HB'}{BB'}(**)\)

\(\left\{\begin{matrix} S_{HAB}=\frac{HC'.AB}{2}\\ S_{ABC}=\frac{CC'.AB}{2}\end{matrix}\right.\) \(\Rightarrow \frac{S_{HAB}}{S_{ABC}}=\frac{HC'}{CC'}(***)\)

Từ \((*); (**); (***)\Rightarrow \frac{HA'}{AA'}+\frac{HB'}{BB'}+\frac{HC'}{CC'}=\frac{S_{HBC}+S_{HCA}+S_{HAB}}{S_{ABC}}=\frac{S_{ABC}}{S_{ABC}}=1\)

Chứng minh gì lạ vậy bạn.

cho cau hoi ko co chung minh ai lam dc

có

\(\dfrac{s_{hbc}}{s_{abc}}=\dfrac{\dfrac{ha'.bc}{2}}{\dfrac{aa'.bc}{2}}=\dfrac{ha'}{aa'}\\ cmtt\\ =>\left\{{}\begin{matrix}\dfrac{s_{ahc}}{s_{abc}}=\dfrac{hb'}{bb'}\\\dfrac{s_{ahb}}{s_{abc}}=\dfrac{hc'}{cc'}\end{matrix}\right.\\ =>\dfrac{ha'}{aa'}+\dfrac{hb'}{bb'}+\dfrac{hc'}{cc'}=\dfrac{s_{hbc}}{s_{abc}}+\dfrac{s_{ahc}}{s_{abc}}+\dfrac{s_{ahb}}{s_{abc}}\\ =\dfrac{s_{abc}}{s_{abc}}\\ =1\left(đpcm\right)\)

vậy ...

chúc may mắn :))

Ban vao trang Đề thi HSG Toán 8 cấp huyện năm 2016-2017 Phòng GD&ĐT Củ Chi

Ý của bạn  là đề bài cho là \(\frac{HA'}{AA'}+\frac{HB'}{BB'}+\frac{HC'}{CC'}=1\)?