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  =  √ [(s−a)(s−b)(s−c)(s−d)]    (Brahmagupta's formula)

so

Area  =  √ (c·d·a·b)