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Britt_d Group Title

In a circle with a 12-inch radius, find the length of a segment joining the midpoint of a 20-inch chord and the center of the circle. x =

  • one year ago
  • one year ago

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  1. jb1515g Group Title
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    |dw:1383721715330:dw|

    • one year ago
  2. jb1515g Group Title
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    Use triangles to solve.

    • one year ago
  3. Britt_d Group Title
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    Pythagorean theorem?

    • one year ago
  4. jb1515g Group Title
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    That's your next step, yes. But it's also important that you understand how I set up that triangle to get to the Pythagorean theorem.

    • one year ago
  5. Britt_d Group Title
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    Ok this is really confusing how did you set it up?

    • one year ago
  6. jb1515g Group Title
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    Alright, so we know that the circle has radius 12, yes? So ANY point on the circle that connects with the center is 12. The chord is 20 inches long, and the definition of chord means that both end points touch the circle. We want to find the length of the segment connecting the MIDPOINT of the chord to the center, meaning that the chord will be split in half. That's where the 10 measurements came from. So one side of the triangle is 10, the other (from the center to the point on the chord) is the radius, or 12. That just leaves x. Clearer?

    • one year ago
  7. Britt_d Group Title
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    Yes so much more clear haha so \[x^{2}+10^{2}=12^{2}\] ?

    • one year ago
  8. jb1515g Group Title
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    yes

    • one year ago
  9. Britt_d Group Title
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    Oh my gosh thank you so much! so it would be \[2\sqrt{22}\] ?

    • one year ago
  10. jb1515g Group Title
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    You might want to check your math on that last part. That's not what I got.

    • one year ago
  11. Britt_d Group Title
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    I'm not to sure what I did wrong......? I did 100-144= 44 and then there isn't a perfect square for 44 so 44\2 = 22 so \[2\sqrt{22}\]

    • one year ago
  12. jb1515g Group Title
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    \[\sqrt{44} =/= 2\sqrt{22}\]

    • one year ago
  13. jb1515g Group Title
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    Evaluate both numbers and see. Sqrt(44) is 6.63, 2*sqrt(22) is 9.38

    • one year ago
  14. jb1515g Group Title
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    Remember that \[\sqrt{ab} = \sqrt{a} * \sqrt{b}\] I think you just simplified the square root wrong.

    • one year ago
  15. Britt_d Group Title
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    Hmm ok so maybe \[2\sqrt{11}\] ?

    • one year ago
  16. jb1515g Group Title
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    Yeah, that's what I got.

    • one year ago
  17. Britt_d Group Title
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    Awesome I just forgot to simplify the 4 thank you!

    • one year ago
  18. jb1515g Group Title
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    Any time. Good job.

    • one year ago
  19. wolf1728 Group Title
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    Basically, you are calculating the length of the apothem. Go to the calculator here: http://1728.org/circsect.htm radius = 12 chord=20 calculator states the apothem = 6.6332 (which is 2 * sqroot(11))

    • one year ago
  20. goformit100 Group Title
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    • one year ago
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