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Let-P-be-an-interior-point-of-a-triangle-ABC-whose-sidelengths-are-26-65-78-The-line-through-P-parallel-to-BC-meets-AB-in-K-and-AC-in-L-The-line-through-P-parallel-to-CA-meets-BC-in-M-and-BA-in-N-




Question Number 21228 by Tinkutara last updated on 16/Sep/17
Let P be an interior point of a triangle  ABC whose sidelengths are 26, 65, 78.  The line through P parallel to BC meets  AB in K and AC in L. The line through  P parallel to CA meets BC in M and BA  in N. The line through P parallel to AB  meets CA in S and CB in T. If KL, MN,  ST, are of equal lengths, find this  common length.
LetPbeaninteriorpointofatriangleABCwhosesidelengthsare26,65,78.ThelinethroughPparalleltoBCmeetsABinKandACinL.ThelinethroughPparalleltoCAmeetsBCinMandBAinN.ThelinethroughPparalleltoABmeetsCAinSandCBinT.IfKL,MN,ST,areofequallengths,findthiscommonlength.

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