A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathmath333

  • one year ago

There are 20 points of which 10 are collinear. Find the maximum number of circles that can be drawn.

  • This Question is Closed
  1. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \(\large \color{black}{\begin{align} & \normalsize \text{There are 20 points of which 10 are collinear.}\hspace{.33em}\\~\\ & \normalsize \text{Find the maximum number of circles that can be drawn.}\hspace{.33em}\\~\\ & a.)\ 900 \hspace{.33em}\\~\\ & b.)\ 800 \hspace{.33em}\\~\\ & c.)\ 700 \hspace{.33em}\\~\\ & d.)\ \normalsize \text{none of these} \end{align}}\)

  2. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it none of these cuz max no circles can be drawn from any two points

  3. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you left out some details. are the points the center, or do they lie on the circumference?

  4. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that info is not given

  5. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    In that case, I have no idea.

  6. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    btw 20C1*20C2+20C2*20C1=900 is given correct

  7. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I guess they don't explain that ?

  8. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no

  9. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    maybe someone else will have some insight on this one.

  10. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    btw, 20C1*20C2+20C2*20C1 would work out to 20*190 + 190*20 that is not 900

  11. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    btw book has many typos in the past

  12. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sry it is 10C1*10C2+10C2*10C1=900

  13. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    it sounds like they want the circle to go through 3 points

  14. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    a circle can be defined by 3 non-collinear points. If we pick 2 points from the line, then to get a circle we have to pick one of the points not on the line that must be how the get the 10C2 * 10C1 term

  15. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i want to make sure if the 2 points circle is not what they want

  16. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you can define a unique circle if you give its center, and a point on the circumference or 3 points on the circumference only the 2nd interpretation makes sense with the answer. (there are an infinite number of circles that have the same two points on their circumference)

  17. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thnks

  18. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I am only guessing on this. There really should be more info on what they are assuming. the other term is consistent with choosing 1 point on the line, and two points from the other set. but we could also choose all 3 points from the non-line set 10C3 and they leave that term out. So I don't really know what is going on.

  19. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    u mean it should be \(900+10C3\)

  20. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, unless you insist the circle must contain a point on the line.

  21. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok i assume ur answer is correct then

  22. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    With the crude information given, I would be tempted to give the following as answer: We have 20 points out of which any three should make a circle, N1=C(20,3)=1140 Out of these, the invalid ones are the choices which have all three falling on the collinear set of 10, so N2=C(10,3)=120 Hence the number of valid circles would be N1-N2=1140-120=\(1020\) This is also equal to include C(10,1)*C(10,2)+C(10,2)*C(10,1)+C(10,3)=450+450+120=1020 The last 120 are those not using the collinear points. That is also why @Phi was expecting more information/restrictions if 900 is the answer. I also believe either the question is incomplete, or the answer did not choose all possibilities.

  23. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.