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Chapter 7 The Menelaus and Ceva Theorems 7.1 7.1 .1 Sig n conve nt ion Let  A  and  B  be tw o distin ct points. A point P  on the line  AB  is said to divide the segment  AB  in the ratio  AP  :  P B, positive if  P  is between  A and  B , and negative if  P  is outside the segment  AB . P  A B  A B P B  A P  AP/PB > 0. -1 < AP/PB < 0.  AP/PB < -1. 7. 1.2 Harmo nic conjugate s Two point s  P  and  Q  on a line  AB  are said to divide the segment  AB harmonically  if they divide the segment in the same ratio, one externally and the other internally: AP P B  = # AQ QB . We shall also say that  P  and Q  are  harmonic conjugates  with respect to the segment  AB. 87

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