A community for students.
Here's the question you clicked on:
 0 viewing
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.
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.

This Question is Closed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7dw:1438159940791:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7Circle 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.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1I remember this proof.... ughhh don't miss it at all >:/

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7That also proves that all circles are similar!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so they are similar because it can be dilated to match the size of the other one?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok so this works for every circle

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7Yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0oh ok thank you sooo much for all of your help you deserve all the medals

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7Since 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
 one year ago
Best ResponseYou've already chosen the best response.0wow i really wish my teacher explained it like you

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7dw:1438160810593:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7im kinda dyslexic today haha @Astrophysics

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i would put circle b and circle c are similar because you can dilate circle b by 1/2

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7Also explain the translation part because you're given the coordinates, so i think your teacher expects you to mess with coordinates too

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Would 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
 one year ago
Best ResponseYou've already chosen the best response.0when you say translation what do you mean

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1well for an isometric transformation .. translation doesn't do anything to the shape.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7I think that can be used, that says circumference scales linearly as diameter is changed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7@thehelpyesineed my first two replies in the top cover the complete proof

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.7you may replace the word "translation" by "move" @thehelpyesineed
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.