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A diagonal splits the quadrilateral into right triangles: Pythagoras and its converse

This type of question, asked 3 times: CDS 2 2020, CDS 1 2026, CDS 2 2026. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2020

    61
    In a quadrilateral ABCD, ∠B=90∘\angle B = 90^\circ and AB2+BC2+CD2−AD2=0AB^2 + BC^2 + CD^2 - AD^2 = 0, then what is ∠ACD\angle ACD equal to ?

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  2. Question 2

    CDS 1 2026

    59
    ABCD is a quadrilateral with sides AB=9AB = 9 cm, BC=40BC = 40 cm, CD=28CD = 28 cm and DA=15DA = 15 cm and one of the diagonals AC=41AC = 41 cm. Which of the following statements is/are correct ? I. The vertices A, B, C and D of the quadrilateral lie on a circle. II. The area of triangle ACD is 126126 cm2^2. Select the answer using the code given below :

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  3. Question 3

    CDS 2 2026

    64
    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 = 454\sqrt{5} cm, DA = 252\sqrt{5} cm and inscribed in a circle. What is the diameter of the circle ? Statement I : The area of the quadrilateral is 44 cm2\text{cm}^2. Statement II : ∠ABC=90∘\angle ABC = 90^\circ. Which one of the following is correct in respect of the above Question and Statements ?

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  4. Question 4

    CDS 2 2026

    80
    In a quadrilateral ABCD, ∠ABC=90∘\angle ABC = 90^\circ and ∠ACD=90∘\angle ACD = 90^\circ. Let AB = p units, BC = q units, AC = r units, CD = s units, AD = t units, where p<q<r<s<t<15p < q < r < s < t < 15. If p, q, r, s and t are integers, then what is the area of the quadrilateral ?

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