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

1 Answer
Mar 25, 2018

drawn

In the figure #Delta ABC# is inscribed in a circle of radius #R# and center #O# and the circle is inscribed in a square #PQRS#.
Obviously the side of the square will be #2R#.

Now in #Delta ABC#,

#BC=a=9,CA=b=10and AB=c=8#

So its semi perimeter #s=(a+b+c)/2=13.5#

So area of #Delta ABC#

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

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

#=>Delta=sqrt(13.5xx4.5xx3.5xx5.5)~~34.2# sq unit

Now #R=(abc)/(4Delta)=(9xx10xx8)/(4xx34.2)~~5.17#unit

So area of the square #-4R^2=4xx5.17^2~~107#sq.unit