PYQ Vault

Perpendicular from the right angle to the hypotenuse = product of legs / hypotenuse

This type of question, asked 6 times: CDS 1 2019, CDS 1 2021, CDS 1 2023, CDS 2 2023, CDS 1 2025, CDS 2 2025. All 6 questions below, oldest first.

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  1. Question 1

    CDS 1 2019

    48
    ABCABC is a triangle right angled at BB. If AB=5AB = 5 cm and BC=10BC = 10 cm, then what is the length of the perpendicular drawn from the vertex BB to the hypotenuse ?

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  2. Question 2

    CDS 1 2021

    88
    ABCABC is a triangle right angled at CC. Let pp be the length of the perpendicular drawn from CC on ABAB. If BC=6BC = 6 cm and CA=8CA = 8 cm, then what is the value of pp?

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  3. Question 3

    CDS 1 2023

    56
    Let ABC be a right-angled triangle with sides 5 cm, 12 cm and 13 cm. If pp is the length of the perpendicular drawn from vertex A on the hypotenuse BC, then what is the value of 13p13p ?

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  4. Question 4

    CDS 2 2023

    84
    In a triangle ABC, angle B=90∘B = 90^\circ and p is the length of the perpendicular from B to AC. If BC = 10 cm and AC = 12 cm, then what is the value of p ?

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  5. Question 5 (case study, 2 parts)

    CDS 1 2025

    ABC is a triangle right-angled at A. Further, AB = 8 cm, BC = 10 cm. D is the point on BC such that AD is perpendicular to BC.
    65
    What is AD equal to ?

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    66
    What is ratio of area of triangle ADC to area of triangle ADB ?

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  6. Question 6

    CDS 2 2025

    72
    ABCABC is a triangle right angled at BB. DD is a point on ACAC such that BDBD is perpendicular to ACAC. If AB=pAB = p and BC=3pBC = \sqrt{3}p, then what is BDBD equal to?

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