In a triangle, the sum of two sides is x and the product of the same two sides is y. If `x^(2)-c^(2)=y,` where c is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle is

Answer

3

Explanation

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`