Given $A(0,0),B(b,0),C(c,a),D(d,a)$. The condition $AC \bot BD$ gives $d=b-\frac{a^{2}}{c}$. Point $O(\frac{bc^{2}}{a^{2}+c^{2}},\frac{abc}{a^{2}+c^{2}})$. The line $AC\ :\ y=\frac{a}{c}x$ with $M(m,\frac{am}{c})$. The condition $BM \bot DM$ gives $m=\frac{bc^{2}-\sqrt{a^{2}bc(a^{2}-bc+c^{2})}}{a^{2}+c^{2}}$. The line $BD\ :\ y=-\frac{c}{a}(x-b)$ with $N(n,\frac{c(b-n)}{a})$. The condition $AN \bot CN$ gives $n=\frac{bc^{2}+\sqrt{a^{2}bc(a^{2}-bc+c^{2})}}{a^{2}+c^{2}}$. I thought $MN\ //\ AB$, but $y_{M}\ \neq\ y_{N}$. After calculations $\frac{ON}{OA}=\frac{OM}{OB}=\frac{MN}{AB}$, so $\triangle OMN \sim \triangle OAB$.