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JEE Main20246 Apr 2024Morning ShiftMathematicsCircleActual

A circle is inscribed in an equilateral triangle of side of length 12 . If the area and perimeter of any square inscribed in this circle are m and n , respectively, then m+n^2 is equal to

Options

  1. A408
  2. B414
  3. C396
  4. D312

Correct answer

A. 408

Step-by-step solution

r = s = 3 a ^2 4 3 a 2 = a 2 3 = 12 2 3 =2 3 aligned & A= r 2 =2 6 & Area = m = A ^2=24 & Perimeter = n =4 ~A =8 6 & m + n ^2=24+384 & =408 aligned

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