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 PQRS cyclic?
Which one of the following is correct in respect of the above Question and the Statements?
- 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
The segment joining consecutive midpoints of any quadrilateral forms a parallelogram; for a rhombus the adjacent mid-segments are perpendicular, so PQRS is a rectangle. Every rectangle is cyclic (its diagonals are diameters of the circumcircle), so the answer needs neither statement, option D. Since the answer never depends on the rhombus's angles, both statements are redundant.