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Sum of the medians compared with the perimeter (inequalities)

This type of question, asked 3 times: CDS 1 2018, CDS 2 2019, CDS 1 2022. All 3 questions below, oldest first.

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  1. Question 1 (case study, 2 parts)

    CDS 1 2018

    Consider the following for the next two (02) questions : In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.
    89
    Which one of the following is correct ?

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    90
    Which one of the following is correct ?

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  2. Question 2

    CDS 2 2019

    90
    Consider the following statements : 1. The perimeter of a triangle is greater than the sum of its three medians. 2. In any triangle ABC, if D is any point on BC, then AB+BC+CA>2ADAB + BC + CA > 2AD. Which of the above statements is/are correct ?

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  3. Question 3

    CDS 1 2022

    77
    Consider the following statements : 1. The sum of any two sides of a triangle is less than twice the median drawn to the third side. 2. The perimeter of a triangle is greater than the sum of the three medians. Which of the above statements is/are correct?

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