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Quadrilateral formed by joining the midpoints of the sides: its shape and area

This type of question, asked 3 times: CDS 1 2017, CDS 2 2018, CDS 1 2026. All 3 questions below, oldest first.

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  1. Question 1

    CDS 1 2017

    75
    Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a

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  2. Question 2

    CDS 2 2018

    74
    Let S be the parallelogram obtained by joining the mid-points of the parallelogram T. Consider the following statements : 1. The ratio of area of T to that of S is 2:12 : 1. 2. The perimeter of S is half of the sum of diagonals of T. Which of the above statements is/are correct ?

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  3. Question 3

    CDS 1 2026

    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 : ∠ABC=120∘\angle ABC = 120^\circ Statement-II : ∠BCD=60∘\angle BCD = 60^\circ Which one of the following is correct in respect of the above Question and the Statements ?

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