Given the trapezoid $ABCD\ :\ A(a,d,B(0,0),C(c,0),D(b,d)$. Choose $P(\lambda,\frac{d\lambda}{a})$. Points $Q(\frac{c\lambda}{a},0)$ and $R(\frac{ab-b\lambda+a\lambda}{a},d)$. The line $QR\ :\ y=\frac{ad}{ab-b\lambda+a\lambda-c\lambda}(x-\frac{c\lambda}{a})$ or $\lambda[y(a-b-c)+cd]=adx-aby$. We must solve the system $\left\{\begin{array}{ll} y(a-b-c)+cd=0 \\ adx-aby =0 \end{array}\right.$ and we find the fixed point $(\frac{bc}{b+c-a},\frac{cd}{b+c-a})$.