anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@ganeshie8
ganeshie8
  • ganeshie8
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ganeshie8
  • ganeshie8
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.

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UsukiDoll
  • UsukiDoll
I remember this proof.... ughhh don't miss it at all >:/
ganeshie8
  • ganeshie8
That also proves that all circles are similar!
anonymous
  • anonymous
so they are similar because it can be dilated to match the size of the other one?
ganeshie8
  • ganeshie8
Exactly!
anonymous
  • anonymous
oh ok so this works for every circle
ganeshie8
  • ganeshie8
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.
anonymous
  • anonymous
oh ok thank you sooo much for all of your help you deserve all the medals
ganeshie8
  • ganeshie8
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".
anonymous
  • anonymous
wow i really wish my teacher explained it like you
ganeshie8
  • ganeshie8
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ganeshie8
  • ganeshie8
im kinda dyslexic today haha @Astrophysics
anonymous
  • anonymous
so i would put circle b and circle c are similar because you can dilate circle b by 1/2
ganeshie8
  • ganeshie8
Also explain the translation part because you're given the coordinates, so i think your teacher expects you to mess with coordinates too
Empty
  • Empty
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?
anonymous
  • anonymous
when you say translation what do you mean
UsukiDoll
  • UsukiDoll
well for an isometric transformation .. translation doesn't do anything to the shape.
ganeshie8
  • ganeshie8
I think that can be used, that says circumference scales linearly as diameter is changed
ganeshie8
  • ganeshie8
@thehelpyesineed my first two replies in the top cover the complete proof
anonymous
  • anonymous
okay thanks
ganeshie8
  • ganeshie8
you may replace the word "translation" by "move" @thehelpyesineed

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