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max of sum of distances of point of semicircle from 3 sides of cyclic ABCD

Source: Rioplatense level 3 p5

June 8, 2019
geometrydistancemaximumsemicirclecyclic quadrilateral

Problem Statement

The quadrilateral ABCDABCD is inscribed in a circle of radius 11, so that ABAB is a diameter of the circumference and CD=1CD = 1. A variable point XX moves along the semicircle determined by ABAB that does not contain CC or DD. Determine the position of XX for which the sum of the distances from XX to lines BC,CDBC, CD and DADA is maximum.
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