2026 · Q64
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : ABCD is a quadrilateral with AB = 6 cm, BC = 8 cm, CD = 4√5 cm, DA = 2√5 cm and inscribed in a circle. What is the diameter of the circle?
Statement IThe area of the quadrilateral is 44 cm².
Statement II∠ABC = 90°.
Which one of the following is correct in respect of the above Question and Statements?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question can be answered even without using both the Statements.
Explanation
By the law of cosines on triangles ABC and ADC sharing diagonal AC, with ∠ADC = 180° − ∠ABC (cyclic), we get (100 − AC²)/96 = −(100 − AC²)/80 since AB² + BC² = CD² + DA² = 100, forcing AC = 10. Then AB² + BC² = AC² makes ∠ABC = 90°, so AC is a diameter of length 10 cm. This uses only the given sides — no statement needed, option D.