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minimum segment of projections of a point in hypotenuse on other sides

Source: Brazilian Mathematical Olympiad 1984 P4

July 27, 2018
geometryright triangleminimumprojectionSegment

Problem Statement

ABCABC is a triangle with ∠A=90o\angle A = 90^o. For a point DD on the side BCBC, the feet of the perpendiculars to ABAB and ACAC are EE andF F. For which point DD is EF EF a minimum?
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