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 midpoints 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: ∠ABC = 120°
Statement-II: ∠BCD = 60°
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
Explanation
Midpoints of sides of any quadrilateral form a parallelogram (Varignon's theorem). For a rhombus, the diagonals are perpendicular, so the Varignon parallelogram PQRS is a rectangle. Every rectangle is cyclic. So the answer is YES, without needing either statement.
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