Triangle ABC is inscribed in a circle inscribed in a square. If AB, AC, and BC are 8, 9, and 10 respectively, determine the exact area of the square.?

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Answer 1 · 2018-03-18T11:30:35

Given that the sides of the #DeltaABC# are

#a=BC=10#

#b=CA=9#

#c=AB=8#

Semi perimeter of the triangle #s=1/2(a+b+c)=13.5#

Area of #DeltaABC#

#Delta=sqrt(s(s-a)(s-b)(s-c))#

#=sqrt(13.5(13.5-10)(13.5-9)(13.5-8))#

#=sqrt(13.5xx3.5xx4.5xx5.5)#sq unit

The circum radius of the triangle is

#R=(abc)/(4Delta)#

So side of the square in which the circle is inscribed will be

#=2*R=(abc)/(2Delta)#

Hence area of the square will be

#=(abc)^2/(4Delta^2)#

#=(10*9*8)^2/(4xx13.5xx3.5xx4.5xx5.5)# sq unit