domingo, 15 de enero de 2017

1137. A dot on the blackboard

    Pepe Chapuzas was erasing the blackboard but there was a white dot that cannot be deleted...

    Dear Teacher:
    If  a ,  b ,  c  and  d  are the four distances from this point to each corner of the blackboard... Is it true that
a+ c2  =  b + d2   ??

    Nina Guindilla (and Pythagoras) proved this equality:

    Dear Teacher:
    If  e ,  f ,  g  and  h  are the four distances from that point to each side of the blackboard... then...
a2  =  e + f 2
b2  =  f 2  + g2
c2  =  g + h2
d2  =  h + e2

     And therefore...
a+ c2  =  e + f 2 + g + h2
b+ d2  =  e + f 2 + g + h2

    Q.E.D.

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