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      Question

      Find the radius of the largest circle that can be

      inscribed in a square, if the rectangle of length 40cm * 20cm is constructed in the corners of the square between the space of square and circle. The three vertices lie on the square and a vertex of the circumference of the circle?
      A 100 cm Correct Answer Incorrect Answer
      B 120 cm Correct Answer Incorrect Answer
      C 150 cm Correct Answer Incorrect Answer
      D 200 cm Correct Answer Incorrect Answer

      Solution

      r² = (r - 40)² + (r - 20)² r² = r² + 1600 - 80r + r² + 400 - 40r r² = 2r² - 120r + 2000 r² - 120r + 2000 = 0 r² - 100r - 20r + 2000 = 0 r(r - 100) - 20(r - 100) = 0 r = 20, 100 r = 100 [20 value is not satisfied]

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