ABCD is a quadrilateral with sides AB = 9 cm, BC = 40 cm, CD = 28 cm and DA = 15 cm and one of the diagonals AC = 41 cm. Which of the following statements is/are correct ? I. The vertices A, B, C and D of the quadrilateral lie on a circle. II. The area of triangle ACD is 126 \text{ cm}^2. Select the answer using the code given below :

Explanation

In \triangle ABC, 9^2 + 40^2 = 1681 = 41^2, so \angle B = 90^\circ. For the quadrilateral to be cyclic, \angle D must be 90^\circ. However, in \triangle ACD, 15^2 + 28^2 = 1009 \neq 41^2, so it's not cyclic (I is false). Using Heron's formula for \triangle ACD, s = (15+28+41)/2 = 42. Area = \sqrt{42(42-15)(42-28)(42-41)} = \sqrt{42 \times 27 \times 14 \times 1} = 126 \text{ cm}^2 (II is true).

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