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

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jb1515g
 2 years ago
Best ResponseYou've already chosen the best response.0Use triangles to solve.

jb1515g
 2 years ago
Best ResponseYou've already chosen the best response.0That'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.

Britt_d
 2 years ago
Best ResponseYou've already chosen the best response.0Ok this is really confusing how did you set it up?

jb1515g
 2 years ago
Best ResponseYou've already chosen the best response.0Alright, 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?

Britt_d
 2 years ago
Best ResponseYou've already chosen the best response.0Yes so much more clear haha so \[x^{2}+10^{2}=12^{2}\] ?

Britt_d
 2 years ago
Best ResponseYou've already chosen the best response.0Oh my gosh thank you so much! so it would be \[2\sqrt{22}\] ?

jb1515g
 2 years ago
Best ResponseYou've already chosen the best response.0You might want to check your math on that last part. That's not what I got.

Britt_d
 2 years ago
Best ResponseYou've already chosen the best response.0I'm not to sure what I did wrong......? I did 100144= 44 and then there isn't a perfect square for 44 so 44\2 = 22 so \[2\sqrt{22}\]

jb1515g
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{44} =/= 2\sqrt{22}\]

jb1515g
 2 years ago
Best ResponseYou've already chosen the best response.0Evaluate both numbers and see. Sqrt(44) is 6.63, 2*sqrt(22) is 9.38

jb1515g
 2 years ago
Best ResponseYou've already chosen the best response.0Remember that \[\sqrt{ab} = \sqrt{a} * \sqrt{b}\] I think you just simplified the square root wrong.

Britt_d
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm ok so maybe \[2\sqrt{11}\] ?

jb1515g
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, that's what I got.

Britt_d
 2 years ago
Best ResponseYou've already chosen the best response.0Awesome I just forgot to simplify the 4 thank you!

wolf1728
 2 years ago
Best ResponseYou've already chosen the best response.0Basically, 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
 2 years ago
Best ResponseYou've already chosen the best response.0A 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/codeofconduct ). Please take a moment to read it.
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