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AP EAMCET202420 May 2024Morning ShiftMathematicsProperties of TrianglesActual

If a circle is inscribed in an equilateral triangle of side a, then the area of any square (in sq. units) inscribed in this circle is

Options

  1. A2 a^2 3
  2. B3 a^2 2
  3. Ca^2 2 3
  4. Da^2 6

Correct answer

D. a^2 6

Step-by-step solution

Area of A B C( )= 3 4 a^2 , Semi-perimeter of A B C(s)= 3 a 2 Radius (r) = s = a 2 3 Diagonal of square PQRS =2 a 2 3 = a 3 Area of square = ( diagonal )^2 2 = a^2 6

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