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Constructing a triangle passing through given points

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January 17, 2011
ratiogeometry unsolvedgeometry

Problem Statement

In a plane three points P,Q,R,P,Q,R, not on a line, are given. Let k,l,mk, l, m be positive numbers. Construct a triangle ABCABC whose sides pass through P,Q,P, Q, and RR such that PP divides the segment ABAB in the ratio 1:k1 : k, QQ divides the segment BCBC in the ratio 1:l1 : l, and RR divides the segment CACA in the ratio 1:m.1 : m.
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