jueves, 16 de febrero de 2017

1275. More special quadrilaterals

    If a quadrilateral is inscribed in a circle and circumscribed about another circle then is a bicentric quadrilateral.
    If  a ,  b ,  c  and  d  are the four sides of a bicentric quadrilateral then its area measures...

    Pepe Chapuzas reasoned as follows:

    Dear Teacher:
    Let  s  be the semiperimeter. Since the quadrilateral is circumscriptible...


a + c  =  b + d  =  s      (Pitot's theorem)

    Since the quadrilateral is inscriptible... 


Area  =   [(sa)(sb)(sc)(sd)]    (Brahmagupta's formula)
so
Area  =  √ (c·d·a·b)

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