## BeccaB003 one year ago Help with chord lengths? Thanks!

1. BeccaB003

2. BeccaB003

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

Sorry, the final answer is actually $20\sqrt{2}$

4. AkashdeepDeb

$$DG^2 = DF^2 + FG^2$$ [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

Thank you! But, why does 2GF^2 = 400? I get a little confused around there.

6. BeccaB003

@AkashdeepDeb

7. AkashdeepDeb

$$DF = FG = GF$$ $$DF^2 + FG^2 = 2 * GF^2 = 2 * DF^2 = 2 * FG^2$$

8. BeccaB003

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

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

Wait, do you mean the curve of AG? AD doesn't curve.

11. BeccaB003

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

Also, does knowing the angle D help you find the arc AG at all?

13. AkashdeepDeb

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

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

I mainly need help knowing how to find arcs and what information you need to find them.

16. AkashdeepDeb

You do not need trig. at all here. My bad. You are right, D will be 90 degrees.

17. AkashdeepDeb

Do you know what the circumference is?

18. BeccaB003

360 degrees

19. AkashdeepDeb

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

Isn't the circumference the length around the whole circle?

21. AkashdeepDeb

Yes, it is.

22. BeccaB003

Isn't that 360 degrees?

23. BeccaB003

$2*\pi*20$

24. AkashdeepDeb

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

But, yes, the angle of the circle is 360. That is, the whole circle!

26. BeccaB003

oh okay. So the circumference is: $2*3.14*20$

27. AkashdeepDeb

Yes.

28. BeccaB003

divided by 4 which is 31.4

29. AkashdeepDeb

Absolutely right!

30. AkashdeepDeb

And that's the length of arc AG.

31. BeccaB003

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

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

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

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

Thank you. I'm sorry you haven't slept yet! It's day time here.

36. BeccaB003

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

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

I need the answer in degrees and not in length.

39. AkashdeepDeb

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

Do you know that 30, 60, 90 triangle rule?

41. BeccaB003

yes

42. AkashdeepDeb

See, triangle ABD. Can you find which angle is which by using the 30, 60, 90 right triangle ratio rule?

43. BeccaB003

angle b is 90 angle a is 30 and angle d is 60

44. AkashdeepDeb

Excellent! So, arc AC is (in degrees)?

45. BeccaB003

120 degrees

46. AkashdeepDeb

And what is arc CE then?

47. BeccaB003

60 degrees!! Thanks! This topic has been hard for me to get a hang of. Thanks for the help!

48. BeccaB003

Get some sleep!! :D

49. AkashdeepDeb

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

Yes, I sometimes don't know where to find proof...thanks for helping me!