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Altitude AD of a triangle: AB^2 - AC^2 = BD^2 - CD^2

This type of question, asked 2 times: CDS 2 2022, CDS 2 2025. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2022

    77
    The perpendicular AD on the base BC of a triangle ABC intersects BC at D so that DB = 3 CD. Which one of the following is correct ?

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  2. Question 2

    CDS 2 2025

    61
    Let ADAD be the altitude of a triangle ABCABC. If (AB+AC)=p(AB + AC) = p, (AB−AC)=q(AB - AC) = q and (BD−CD)=r(BD - CD) = r, then what is BCBC equal to?

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