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BeccaB003

  • one year ago

Help with chord lengths? Thanks!

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  1. BeccaB003
    • one year ago
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  2. BeccaB003
    • one year ago
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    I need help knowing how to find GE. I know the answer is \[20\sqrt{3}\] but I don't know how to find that answer!

  3. BeccaB003
    • one year ago
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    Sorry, the final answer is actually \[20\sqrt{2}\]

  4. AkashdeepDeb
    • one year ago
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    \(DG^2 = DF^2 + FG^2\) [Because of Pythagorus' Theorem] \(DF = FG\) [Given] \(DG = 20\) [Given] \(2GF^2 = 400\) \(GF^2 = 200\) \(GF = 10 \sqrt{2}\) Because, the radius perpendicular to the chord also bisects it, \(GE = 2GF\) Hence, \(GE = 2 * 10 \sqrt{2}\) \(GE = 20 \sqrt{2}\)

  5. BeccaB003
    • one year ago
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    Thank you! But, why does 2GF^2 = 400? I get a little confused around there.

  6. BeccaB003
    • one year ago
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    @AkashdeepDeb

  7. AkashdeepDeb
    • one year ago
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    \(DF = FG = GF\) \(DF^2 + FG^2 = 2 * GF^2 = 2 * DF^2 = 2 * FG^2\)

  8. BeccaB003
    • one year ago
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    Thank you! :D Can you help me find the measure of the arc AG in the same image? Also, I don't really understand the difference between the AG arc and the angle D. How do you transition between the two? Thanks!!

  9. AkashdeepDeb
    • one year ago
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    Angle D is just the angle. It is like the angle your clock is forming with the minute and the hour hand. Arc AG is an actual length. It's the length of the arc if you place a string along the curve AD.

  10. BeccaB003
    • one year ago
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    Wait, do you mean the curve of AG? AD doesn't curve.

  11. BeccaB003
    • one year ago
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    What I mean is, you said, if you place a string along the curve AD. AD isn't a curve. Did you mean AG?

  12. BeccaB003
    • one year ago
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    Also, does knowing the angle D help you find the arc AG at all?

  13. AkashdeepDeb
    • one year ago
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    Yes, I meant AG and not AD. Also, yes, you do need to know angle D to find arc AG's length. Do you know how to find out angle D?

  14. BeccaB003
    • one year ago
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    Yes, angle D is 90 degrees because angle GDE is 90 degrees and AE is the diametor which is 180 degrees. I do know basic ratios but have had a harder time working with them.

  15. BeccaB003
    • one year ago
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    I mainly need help knowing how to find arcs and what information you need to find them.

  16. AkashdeepDeb
    • one year ago
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    You do not need trig. at all here. My bad. You are right, D will be 90 degrees.

  17. AkashdeepDeb
    • one year ago
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    Do you know what the circumference is?

  18. BeccaB003
    • one year ago
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    360 degrees

  19. AkashdeepDeb
    • one year ago
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    No, the length of the circumference is = \(2 * \pi * r\) Where \(r\) is the radius. Here, 20. So, find the circumference. Aldo, if D is 90 degrees, it basically divides the entire circle into 4 equal parts (or 4 equal quadrants). Hence, the length of the arc AG can be found out by diving the circumference of the circle by 4. :)

  20. BeccaB003
    • one year ago
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    Isn't the circumference the length around the whole circle?

  21. AkashdeepDeb
    • one year ago
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    Yes, it is.

  22. BeccaB003
    • one year ago
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    Isn't that 360 degrees?

  23. BeccaB003
    • one year ago
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    \[2*\pi*20\]

  24. AkashdeepDeb
    • one year ago
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    That's not the length. That's the measure of the angle. Just like when it is 6 am, the minute hand and the hour hand form 180 degree between them, and that's just the angle measure. The circumference of a circle is defined as the length of the distance around the circle.

  25. AkashdeepDeb
    • one year ago
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    But, yes, the angle of the circle is 360. That is, the whole circle!

  26. BeccaB003
    • one year ago
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    oh okay. So the circumference is: \[2*3.14*20\]

  27. AkashdeepDeb
    • one year ago
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    Yes.

  28. BeccaB003
    • one year ago
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    divided by 4 which is 31.4

  29. AkashdeepDeb
    • one year ago
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    Absolutely right!

  30. AkashdeepDeb
    • one year ago
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    And that's the length of arc AG.

  31. BeccaB003
    • one year ago
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    These problems are just practice problems so i have the correct answers and it says it's 90 degrees. How do you change 31.4 to degrees?

  32. AkashdeepDeb
    • one year ago
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    I think you're getting confused here. Angle and Length IS NOT the same thing, so you cannot CHANGE length to degrees. |dw:1434411475094:dw| I think, what they means is, the angle of the arc AG = 90 degrees. But the length of the arc AG = 31.4 units.

  33. BeccaB003
    • one year ago
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    Oh okay! I see. :) What about measure of the arc CE? I'll walk through the steps and you see if I do it right. Is that okay?

  34. AkashdeepDeb
    • one year ago
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    Yes. Fine. It's 3:45 am here, where I live (And I haven't slept yet). I am here for another 10 minutes.

  35. BeccaB003
    • one year ago
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    Thank you. I'm sorry you haven't slept yet! It's day time here.

  36. BeccaB003
    • one year ago
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    Angle ADC looks like it is split into to equal parts. Angle EDC looks the same. line AE is 180 degrees so divided by three it is 60 degrees.

  37. BeccaB003
    • one year ago
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    I know that is not the correct way to solving it but they don't give is the any angle degrees. I also can't see any angles that are similar to those angles.

  38. BeccaB003
    • one year ago
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    I need the answer in degrees and not in length.

  39. AkashdeepDeb
    • one year ago
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    Try to reason when you see the figures and never put conclude from how the figure 'looks'. arc ADB and arc BDC are same because DB bisected AC. Also, in no way, can we say that arc CE is 60 degrees because there is not proof for it yet.

  40. AkashdeepDeb
    • one year ago
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    Do you know that 30, 60, 90 triangle rule?

  41. BeccaB003
    • one year ago
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    yes

  42. AkashdeepDeb
    • one year ago
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    See, triangle ABD. Can you find which angle is which by using the 30, 60, 90 right triangle ratio rule?

  43. BeccaB003
    • one year ago
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    angle b is 90 angle a is 30 and angle d is 60

  44. AkashdeepDeb
    • one year ago
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    Excellent! So, arc AC is (in degrees)?

  45. BeccaB003
    • one year ago
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    120 degrees

  46. AkashdeepDeb
    • one year ago
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    And what is arc CE then?

  47. BeccaB003
    • one year ago
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    60 degrees!! Thanks! This topic has been hard for me to get a hang of. Thanks for the help!

  48. BeccaB003
    • one year ago
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    Get some sleep!! :D

  49. AkashdeepDeb
    • one year ago
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    Yes! That's right. See, how, initially, you had said 60 degrees, without the proof, and now you said the same thing with a more established proof with more understanding. Well done!

  50. BeccaB003
    • one year ago
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    Yes, I sometimes don't know where to find proof...thanks for helping me!

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