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Prove that L1=L2=L3 - [IMO LongList 1971]

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January 1, 2011
geometry proposedgeometry

Problem Statement

In a triangle P1P2P3P_1P_2P_3 let PiQiP_iQ_i be the altitude from PiP_i for i=1,2,3i = 1, 2,3 (QiQ_i being the foot of the altitude). The circle with diameter PiQiP_iQ_i meets the two corresponding sides at two points different from Pi.P_i. Denote the length of the segment whose endpoints are these two points by li.l_i. Prove that l1=l2=l3.l_1 = l_2 = l_3.
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