如图,RT△ABC中,∠ACB=90°,AC=a,BC=b,CD⊥AB,且CD=h.试说明1/a²+1/b²=1/h².
问题描述：
如图,RT△ABC中,∠ACB=90°,AC=a,BC=b,CD⊥AB,且CD=h.试说明1/a²+1/b²=1/h².
答
证明:,∠ACB=90°;CD⊥AB.则:2S⊿ABC=AC*BC=AB*CD,即:ab=ch;则:(ab)^2=(ch)^2,a^2b^2=c^2h^2;故:(h^2*c^2)/(a^2b^2)=1;又c^2=a^2+b^2.∴[h^2(a^2+b^2)]/(a^2b^2)=1;(h^2a^2/(a^2b^2)+(h^2b^2)/(a^2b^2)=1;h^2/b^2+...