Question Number 143537 by 0731619 last updated on 15/Jun/21
Answered by mr W last updated on 15/Jun/21
$$\frac{{AB}+{BE}}{{BE}}=\frac{{AD}}{{BC}}=\frac{{a}}{{b}} \\ $$$$\frac{{AB}}{{BE}}=\frac{{a}−{b}}{{b}} \\ $$$$\frac{{GE}}{{AD}}=\frac{{BE}}{{AB}}=\frac{{b}}{{a}−{b}} \\ $$$$\Rightarrow{GE}=\frac{{ab}}{{a}−{b}} \\ $$$${similarly} \\ $$$${EH}=\frac{{ab}}{{a}−{b}} \\ $$$$\Rightarrow{GH}=\frac{\mathrm{2}{ab}}{{a}−{b}} \\ $$