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Consider a triangle A B C and let a , ba...

Consider a triangle `A B C` and let `a , ba n dc` denote the lengths of the sides opposite to vertices `A , B ,a n dC` , respectively. Suppose `a=6,b=10 ,` and the area of triangle is `15sqrt(3)dot` If `/_A C B` is obtuse and if `r` denotes the radius of the incircle of the triangle, then the value of `r^2` is

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The correct Answer is:
3
sin `C=sqrt3/2` and C is given to be obtuse.
`C=(2pi)/2=sqrt(a^(2)+b^(2)-"2ab cos C")`
`=sqrt(6^(2)+10^(2)-2xx6xx10xx"cos"(2pi)/3)=14`
`:.r=Delta/srArrr^(2)=(225xx3)/(((6+10+14)/2)^(2))=3`
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