anonymous
  • anonymous
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 =
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
Use triangles to solve.
anonymous
  • anonymous
Pythagorean theorem?

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anonymous
  • anonymous
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.
anonymous
  • anonymous
Ok this is really confusing how did you set it up?
anonymous
  • anonymous
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?
anonymous
  • anonymous
Yes so much more clear haha so \[x^{2}+10^{2}=12^{2}\] ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Oh my gosh thank you so much! so it would be \[2\sqrt{22}\] ?
anonymous
  • anonymous
You might want to check your math on that last part. That's not what I got.
anonymous
  • anonymous
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 \[2\sqrt{22}\]
anonymous
  • anonymous
\[\sqrt{44} =/= 2\sqrt{22}\]
anonymous
  • anonymous
Evaluate both numbers and see. Sqrt(44) is 6.63, 2*sqrt(22) is 9.38
anonymous
  • anonymous
Remember that \[\sqrt{ab} = \sqrt{a} * \sqrt{b}\] I think you just simplified the square root wrong.
anonymous
  • anonymous
Hmm ok so maybe \[2\sqrt{11}\] ?
anonymous
  • anonymous
Yeah, that's what I got.
anonymous
  • anonymous
Awesome I just forgot to simplify the 4 thank you!
anonymous
  • anonymous
Any time. Good job.
wolf1728
  • wolf1728
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))
goformit100
  • goformit100
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