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

Let P be an interior point of a triangle

A B C whose sidelengths are 26, 65, 78 .

The line through P parallel to B C meets

A B in K and A C in L . The line through

P parallel to C A meets B C in M and B A

in N . The line through P parallel to A B

meets C A in S and C B in T . If K L, M N,

S T, are of equal lengths, find this

common length .