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Britt_d

  • 2 years ago

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 =

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  1. jb1515g
    • 2 years ago
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    |dw:1383721715330:dw|

  2. jb1515g
    • 2 years ago
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    Use triangles to solve.

  3. Britt_d
    • 2 years ago
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    Pythagorean theorem?

  4. jb1515g
    • 2 years ago
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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.

  5. Britt_d
    • 2 years ago
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    Ok this is really confusing how did you set it up?

  6. jb1515g
    • 2 years ago
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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?

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

  8. jb1515g
    • 2 years ago
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    yes

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

  10. jb1515g
    • 2 years ago
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    You might want to check your math on that last part. That's not what I got.

  11. Britt_d
    • 2 years ago
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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 \[2\sqrt{22}\]

  12. jb1515g
    • 2 years ago
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    \[\sqrt{44} =/= 2\sqrt{22}\]

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

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

  15. Britt_d
    • 2 years ago
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    Hmm ok so maybe \[2\sqrt{11}\] ?

  16. jb1515g
    • 2 years ago
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    Yeah, that's what I got.

  17. Britt_d
    • 2 years ago
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    Awesome I just forgot to simplify the 4 thank you!

  18. jb1515g
    • 2 years ago
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    Any time. Good job.

  19. wolf1728
    • 2 years ago
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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))

  20. goformit100
    • 2 years ago
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    A warm Welcome to OpenStudy. I can help guide you through this useful site. You can ask your questions to me or you can message me. Please use the chat for off topic questions. Remember to give the person who helped you a medal by clicking on "Best Answer". We follow a code of conduct, ( http://openstudy.com/code-of-conduct ). Please take a moment to read it.

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