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In the mini-question, does choice iv.) not work?

Module 2 Day 7 Challenge Part 4
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  • T
    The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
    last edited by debbie Jul 9, 2020, 1:06 AM Jul 7, 2020, 3:15 PM

    Module 2 Week 2 Day 7 Challenge Part 4

    In the mini-question, does choice iv. not work? I think it does...

    The Blade Dancer
    League of Legends, Valorant: Harlem Charades (#NA1)
    Discord: Change nickname if gay#7585

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      nastya MOD M0 M1 M2 M3 M4 M5
      last edited by Jul 8, 2020, 2:56 AM

      Hi @The-Rogue-Blade!

      In the mini-question, the answer choice IV\text{IV}IV will work if we change it to: "If a point cuts a chord in half, then the Power of a Point formula gives us: ... iv) that the distance from the point to the center of the circle gets smaller as AB‾\overline{AB}AB gets bigger". But in our answer choice IV\text{IV}IV we have smaller instead, which makes this statement wrong. Just imagine how you move this chord and think of it one more time, and then you'll get it 🙂

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        The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
        last edited by Jul 8, 2020, 5:22 PM

        There's a difference?

        The Blade Dancer
        League of Legends, Valorant: Harlem Charades (#NA1)
        Discord: Change nickname if gay#7585

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        • N
          nastya MOD M0 M1 M2 M3 M4 M5
          last edited by debbie Jul 9, 2020, 1:10 AM Jul 8, 2020, 9:07 PM

          Well, obviously, there is 🙂
          Let's take a closer look together.

          Here we have our chord AB‾\overline{AB}AB with its midpoint PPP and a circle with its center O:O:O:
          M2D7C4-hmm-0.jpg
          All points that have distance to the center of our circle that is smaller or equal to the distance from point PPP to the center OOO are points in the smaller purple circle:
          M2D7C4-hmm-1.jpg
          So, all the chords AiBi‾\overline{A_iB_i}Ai​Bi​​ have their midpoint PiP_iPi​ not further than point PPP from the center OOO (see diagram below). To the contrary, all the chords CiDi‾\overline{C_iD_i}Ci​Di​​ have their midpoint RiR_iRi​ further than point PPP to the center O:O:O:
          M2D7C4-hmm-2.jpg
          As we can see from these diagrams, all the AiBi‾\overline{A_iB_i}Ai​Bi​​ chords are bigger than the chords CiDi‾.\overline{C_iD_i}.Ci​Di​​. So the distance\text{\color{blue}\it{distance}}distance from the middle point to the center of the circle gets smaller\text{\color{blue}\bf{smaller}}smaller as the chord\text{\color{blue}\it{chord}}chord gets bigger\text{\color{blue}\bf{bigger}}bigger, while when the chord\text{\color{green}\it{chord}}chord gets smaller\text{\color{green}\bf{smaller}}smaller, the distance\text{\color{green}\it{distance}}distance gets bigger\text{\color{green}\bf{bigger}}bigger. That is why the statement "the distance\text{\color{darkred}\it{distance}}distance gets smaller\text{\color{darkred}\bf{smaller}}smaller as chord\text{\color{darkred}\it{chord}}chord gets smaller\text{\color{darkred}\bf{smaller}}smaller" is wrong.\text{\color{red}{wrong}}.wrong.

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            The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
            last edited by Jul 9, 2020, 3:33 PM

            ooooooooh thanks

            The Blade Dancer
            League of Legends, Valorant: Harlem Charades (#NA1)
            Discord: Change nickname if gay#7585

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