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    In the mini question, why can't it be AE x AF= BC squared?

    Module 2 Day 8 Your Turn Part 2
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    • The Blade DancerT
      The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
      last edited by debbie

      Module 2 Week 2 Day 8 Your Turn Part 2

      In the mini question, why can't it be AE x AF= BC squared?

      The Blade Dancer
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      debbieD 1 Reply Last reply Reply Quote 2
      • debbieD
        debbie ADMIN M0★ M1 M5 @The Blade Dancer
        last edited by debbie

        @The-Rogue-Blade This is a good question! If we take the Power of a Point Theorem literally, then the segments that we are multiplying together should live up to the name "Power of a Point"; they should all emanate from the same point.

        M2W2D8-y-part-2-power-of-point-why-not-ae-times-af-equals-bc-squared.png

        In the above illustration, the correct answer is shown:

        $$ CF \times CE = (BC)^2 $$

        Now consider \(\overline{AE}\) and \(\overline{AF};\) these segments emanate from point \(A,\) but the segment \(\overline{BC}\) emanates from a \(\textcolor{red}{\text{different}}\) point, \(C.\) We have not one point, but \(2\) points.

        M2W2D8-y-part-2-power-of-point-why-not-ae-times-af-equals-bc-squared2.png

        Unfortunately, it's not called "Power of Two Points," so

        $$ AE \times AF \neq (BC)^2 $$

        🙂

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