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Construct triangle ABC - ILL 1990 MON4

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September 18, 2010
combinatorics proposedcombinatorics

Problem Statement

Given points A,M,M1A, M, M_1 and rational number λ≠−1\lambda \neq -1. Construct the triangle ABCABC, such that MM lies on BCBC and M1M_1 lies on B1C1B_1C_1 (B1,C1B_1, C_1 are the projections of B,CB, C on AC,ABAC, AB respectively), and BMMC=B1M1M1C1=λ.\frac{BM}{MC}=\frac{B_1M_1}{M_1C_1}=\lambda.
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