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Question Number 21228 by Tinkutara last updated on 16/Sep/17

$$\mathrm{Let}P\mathrm{be}\mathrm{an}\mathrm{interior}\mathrm{point}\mathrm{of}\mathrm{a}\mathrm{triangle}$$$$ABC\mathrm{whose}\mathrm{sidelengths}\mathrm{are}26,65,78.$$$$\mathrm{The}\mathrm{line}\mathrm{through}P\mathrm{parallel}\mathrm{to}BC\mathrm{meets}$$$$AB\mathrm{in}K\mathrm{and}AC\mathrm{in}L.\mathrm{The}\mathrm{line}\mathrm{through}$$$$P\mathrm{parallel}\mathrm{to}CA\mathrm{meets}BC\mathrm{in}M\mathrm{and}BA$$$$\mathrm{in}N.\mathrm{The}\mathrm{line}\mathrm{through}P\mathrm{parallel}\mathrm{to}AB$$$$\mathrm{meets}CA\mathrm{in}S\mathrm{and}CB\mathrm{in}T.\mathrm{If}KL,MN,$$$$ST,\mathrm{are}\mathrm{of}\mathrm{equal}\mathrm{lengths},\mathrm{find}\mathrm{this}$$$$\mathrm{common}\mathrm{length}.$$

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