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1/x = 1/AB +1/AC

Source: ItaMO 2012, P1

May 21, 2012
geometryangle bisectorsimilar trianglesgeometry proposed

Problem Statement

On the sides of a triangle ABCABC right angled at AA three points D,ED, E and FF (respectively BC,ACBC, AC and ABAB) are chosen so that the quadrilateral AFDEAFDE is a square. If xx is the length of the side of the square, show that 1x=1AB+1AC\frac{1}{x}=\frac{1}{AB}+\frac{1}{AC}
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