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anonymous

  • one year ago

Circle B has a center of (-1, 5) and a radius of 4. Circle D has a center of (7, 4) and a radius of 2. Prove that the two circles are similar.

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  1. anonymous
    • one year ago
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    @ganeshie8

  2. ganeshie8
    • one year ago
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    |dw:1438159940791:dw|

  3. ganeshie8
    • one year ago
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    Circle D can be obtained from circle B by a translation of 8 units to right and 1 units down, followed by a dilation with scale factor of 1/2. Since B can be transformed into D just by translation and dilation, both the circles are similar.

  4. UsukiDoll
    • one year ago
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    I remember this proof.... ughhh don't miss it at all >:/

  5. ganeshie8
    • one year ago
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    That also proves that all circles are similar!

  6. anonymous
    • one year ago
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    so they are similar because it can be dilated to match the size of the other one?

  7. ganeshie8
    • one year ago
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    Exactly!

  8. anonymous
    • one year ago
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    oh ok so this works for every circle

  9. ganeshie8
    • one year ago
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    Yes, coordinates are there just to make the analysis simple. That translation part is not really required. We could simply argue that scaling the circle B by a factor of 1/2 produces the circle D. So both the circles are similar.

  10. anonymous
    • one year ago
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    oh ok thank you sooo much for all of your help you deserve all the medals

  11. ganeshie8
    • one year ago
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    Since any circle can be obtained from any other circle by scaling by a factor of \(\dfrac{r}{r'}\), we can conclude that "all circles are similar".

  12. anonymous
    • one year ago
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    wow i really wish my teacher explained it like you

  13. ganeshie8
    • one year ago
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    |dw:1438160810593:dw|

  14. ganeshie8
    • one year ago
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    im kinda dyslexic today haha @Astrophysics

  15. anonymous
    • one year ago
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    so i would put circle b and circle c are similar because you can dilate circle b by 1/2

  16. ganeshie8
    • one year ago
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    Also explain the translation part because you're given the coordinates, so i think your teacher expects you to mess with coordinates too

  17. Empty
    • one year ago
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    Would it also be considered a proof that all circles are similar since the formula \[\pi = \frac{C}{d}\] is a constant? No matter how large the circle is or where it is, \(\pi\) doesn't depend on it?

  18. anonymous
    • one year ago
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    when you say translation what do you mean

  19. UsukiDoll
    • one year ago
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    well for an isometric transformation .. translation doesn't do anything to the shape.

  20. ganeshie8
    • one year ago
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    I think that can be used, that says circumference scales linearly as diameter is changed

  21. ganeshie8
    • one year ago
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    @thehelpyesineed my first two replies in the top cover the complete proof

  22. anonymous
    • one year ago
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    okay thanks

  23. ganeshie8
    • one year ago
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    you may replace the word "translation" by "move" @thehelpyesineed

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