ILL 1990 Problem 55

Given points $A, M, M_1$ and rational number $\lambda \neq -1$ . Construct the triangle $ABC$ , such that $M$ lies on $BC$ and $M_1$ lies on $B_1C_1$ ( $B_1, C_1$ are the projections of $B, C$ on $AC, AB$ respectively), and $\frac{BM}{MC}=\frac{B_1M_1}{M_1C_1}=\lambda.$