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In a triangle, the sum of lengths of two...

In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If `x^2-c^2=y`, where c is the length of the third side of the triangle, then the circumradius of the triangle is `c/sqrtk`. The value of k is _________.

Text Solution

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The correct Answer is:
3
a+b=x and ab =y
Also `x^2-c^2=y`
`cos C=(a^2+b^2-c^2)/(2ab)=((a+b)^2-2ab-c^2)/(2ab)=(x^2-2y-(x^2-y))/(2y)=-1/2`
`rArr cos C = -1/2 rArr angleC=120^@`
So , circumradius `R=c/(2 sin C)=c/(2 sqrt3/2)=c/sqrt3`
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