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minimum length segment constructions, parallel related

Source: Sharygin 2005 IX CR 13

August 19, 2019
geometryminimumSegmentconstruction

Problem Statement

A triangle ABCABC and two lines ℓ1,ℓ2\ell_1, \ell_2 are given. Through an arbitrary point DD on the side ABAB, a line parallel to ℓ1\ell_1 intersects the ACAC at point EE and a line parallel to ℓ2\ell_2 intersects the BCBC at point FF. Construct a point DD for which the segment EFEF has the smallest length.
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