PYQ Vault

Right triangle with a midpoint or trisection point on a leg: Pythagoras on the line from the opposite vertex

This type of question, asked 4 times: CDS 2 2020, CDS 2 2021, CDS 2 2025, CDS 1 2026. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2020

    87
    ABC is a triangle right-angled at C. Let P be any point on AC and Q be any point on BC. Which of the following statements is/are correct ? 1. AQ2+BP2=AB2+PQ2AQ^2 + BP^2 = AB^2 + PQ^2 2. AB=2PQAB = 2PQ Select the correct answer using the code given below :

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  2. Question 2 (case study, 3 parts)

    CDS 2 2021

    Consider the following for the next three (03) items that follow : ABCABC is a triangle with AB=1.6AB = 1.6 cm, BC=6.3BC = 6.3 cm and CA=6.5CA = 6.5 cm. Let PP and QQ be the mid-points of ABAB and BCBC respectively.
    86
    What is AB2+4BQ2AB^2 + 4BQ^2 equal to ?

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    87
    What is AQ2+CP2AQ^2 + CP^2 equal to ?

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    88
    What is 4(CP2−AQ2)4(CP^2 - AQ^2) equal to ?

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  3. Question 3

    CDS 2 2025

    63
    ABCABC is a triangle right angled at BB. PP is the midpoint of ABAB and QQ is the midpoint of BCBC. Consider the following : I. AQ=73AQ = \sqrt{73} units II. CP=52CP = \sqrt{52} units Which of the above is/are required to determine the area of the triangle?

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  4. Question 4

    CDS 1 2026

    56
    ABC is a triangle right-angled at B. Points M and N trisect BC. If AM=6AM = 6 cm and AN=9AN = 9 cm, then what is AC equal to ?

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  5. Question 5

    CDS 1 2026

    55
    ABC is a triangle right-angled at C. Let P be the midpoint of BC. If AP=413AP = 4\sqrt{13} cm and AB=20AB = 20 cm, then what is the perimeter of the triangle ABC ?

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