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Value of k for which four given points lie on a circle

The same question, asked 2 times: 27 Jan 2024*, 3 Apr 2025. Every wording below, oldest first.

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  1. Question 1

    27 Jan 2024

    72
    Four distinct points (2k,3k),(1,0),(0,1)(2k,3k),(1,0),(0,1) and (0,0)(0,0) lie on a circle for kk equal to :

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  2. Question 2

    3 Apr 2025

    128
    If the four distinct points (4,6),(−1,5),(0,0)(4,6),( - 1,5),(0,0) and ( k,3kk,3k ) lie on a circle of radius rr, then 10k+r210k+r^{2} is equal to.

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