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

a² + c²  =  b²  + 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  =  e²  + f ²
b²  =  f ²  + g²
c²  =  g²  + h²
d²  =  h²  + e²

     And therefore...

a² + c²  =  e²  + f ² + g²  + h²
b² + d²  =  e²  + f ² + g²  + h²

    Q.E.D.