Question

已知：CD为Rt△ABC的斜边上的高，且BC=a，AC=b，AB=c，CD=h（如图）．求证：[1a2+1b2＝1h2．

Answer 1

a*b=c*h

a^2*b^2=c^2*h^2

(a^2*b^2)/(a^2*+b^2)=h^2

(a^2*+b^2)/(a^2*b^2)=1/h^2

1/a^2+1/b^2=1/h^2