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