74. A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : P, Q, R and S are respectively the mid-points of sides AB, BC, CD, DA of a rhombus ABCD. These points are joined to form a quadrilateral PQRS. Is the quadrilateral cyclic ? Statement-I : \angle ABC = 120^\circ Statement-II : \angle BCD = 60^\circ
- A. The Question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- B. The Question can be answered by using either Statement alone
- C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- D. The Question can be answered even without using both the Statements ✓
Correct Answer: D. The Question can be answered even without using both the Statements
Explanation
By Varignon's Theorem, joining the midpoints of any rhombus forms a rectangle. Since all rectangles are cyclic quadrilaterals, the answer is always yes regardless of the specific angles of the rhombus.
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