A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Will medal and fan Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency. 2r r² r√2

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

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

    Find the coordinates of the other endpoint if the midpoint is M(8, 2) and the other endpoint is P(5, 6). (6.5, 4) (21, 10) (11, -2)

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

    |dw:1439227683307:dw| Use Pythagorean Theorem to find length of chord AB

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

    i dont know how..

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

    Triangle AOB is a right triangle. The lengths of the sides are related byt the Pythagorean Theorem. If a right triangle has legs of lengths a and b, and a hypotenuse of length c, these lengths are related by\[a^2 + b^2 = c^2\]Have you seen this before?

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

    no...

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

    May I ask what grade you're in and what course you're working on?

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

    im in 11 and in geometry but im doing online math this summer....

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

    OK. You know what a right triangle is, right?

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

    yes.

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

    Can you identify which sides are the legs and which side is the hypotenuse?

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

    i think so

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

    OK. In the figure I drew, which side is the hypotenuse?

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

    AB?

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

    That's right.

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

    So the other two sides are the legs. Both of these legs are \(r\) unit in length. Do you see where that comes from?

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

    ya

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

    Good.

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

    The Pythagorean Theorem says that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. In our diagram\[\left( AB \right)^2 = \left( AO \right)^2 + \left( OB \right)^2\]Do you understand so far?

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

    no u lost me

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

    \(AB^2\) is the length of the hypotenuse squared. OK?

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

    ok

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

    \(AO^2\) is the length of one of the legs squared. \(OB^2\) is the length of the other leg squared. OK?

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

    ok

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

    Is there an easier way of learning this?

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

    Now, for any right triangle, the lengths of the sides are related, no matter the size. The relationship is, as stated earlier\[\left( AB \right)^2 = \left( AO \right)^2 + \left( OB \right)^2\]Now, we know that the lengths of the legs (AO & OB) are equal to \(r\). So, substituting that value in, we get\[\left( AB \right)^2 = r^2 + r^2 = 2r^2\]Understand?

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

    no not really.. Im really slow with math.. ive never been any good

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

    If \[\left( AO \right) = r\]then \[\left( AO \right)^2 = r^2\]OK?

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

    ok

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

    And if \[\left( OB \right) =r\]then\[\left( OB \right)^2 = r^2\]Then by adding them together\[\left( AB \right)^2 + \left( OB \right)^2 = r^2 + r^2\]Still with me?

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

    um kinda

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

    Well if \[AO^2 = r^2\] and \[OB^2 = r^2\]then \[AO^2 + OB^2 = r^2 + r^2\]

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

    okay

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

    Now \[r^2 + r^2 = 2r^2\]You OK with that?

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

    yas

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

    Alright. Putting all of that together, we have\[AB^2 = AO^2 + OB^2\]\[AB^2 = r^2 + r^2\]\[AB^2 = 2r^2\]Now the question requires that we solve for AB. To do that, you need to take the square root of both sides. Can you do that?

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

    i dont think so

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

    What is the square root of AB^2?

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

    umm.. No clue. Im going into all this blind

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

    What is the square root of any number squared? If 2^2 = 4, what is the square root of 4?

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

    2??

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

    Right. And if 3^2 = 9, the square root of 9 is 3. So the square root of any number squared is that number. Now just do it with a variable instead of a number. So what is the square root of AB^2?

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

    ohhh okay

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

    So\[AB^2 = 2r^2\]\[\sqrt{AB^2} = \sqrt{2r^2}\]\[AB = \sqrt{2} \sqrt{r^2}\]And what is the square root of r^2?

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

    umm i have no clue

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

    We just covered it. The square root of any number squared is that same number. So the square root of r^2 is r. So your answer is\[AB = r \sqrt{2}\]

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

    ohhh okay thank u soo much

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

    You're welcome.

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

    thats what i had too!!!!

  50. 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.