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MHT CET202312 May 2023Morning ShiftMathematicsApplication of DerivativesActual

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

Options

  1. Ac 3
  2. Bc 3
  3. C3 2 y
  4. Dy 3

Correct answer

B. c 3

Step-by-step solution

Let a and b be the lengths of two sides of a triangle. According to the given condition, aligned & a + b =x and ab =y & x^2- c ^2=y ( a + b )^2- c ^2= ab & a^2+b^2+2 a b-c^2=a b & a^2+b^2-c^2=-a b & a ^2+ b ^2- c ^2 2 ab =- 1 2 & C = 1 2 & C = 2 3 & circumradius = c 2 C = c 2 ( 2 3 ) = c 3 & aligned

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