2026 · Q59
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?
- IThe vertices A, B, C and D of the quadrilateral lie on the circle.
- IIThe area of triangle ACD is 126 cm². Select the answer using the code given below:
Elementary MathematicsQuadrilaterals and Polygons
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
Since 9²+40²=41², ΔABC is right-angled at B. But 15²+28²=1009≠41², so ∠ADC≠90° and A,B,C,D are not concyclic — I is incorrect. By Heron's formula with s=42, area(ΔACD)=√(42·1·14·27)=126 cm² — II is correct. Only II is correct, option B.