## anonymous one year ago Help please.... If the diameter of the circle is 36, what is the length of arc ABC? A. 8 B. 8pi C. 28pi D. 32pi E. 56pi

1. anonymous

|dw:1442538379561:dw|

2. johnweldon1993

Well remember: $\large s = r\theta$ The arc length is equal to the radius of the circle times the angle given in radians So first, what is the radius? And what is the angle in radians?

3. anonymous

18

4. anonymous

what do you mean by the angle in radian?

5. anonymous

Can you tell me what they mean when they say "An inscribed angle is aways half the central angel."

6. johnweldon1993

Okay hang on...lets go one by one lol...So first...the "inscribed angle is always half the central angle" Lets look at a circle

7. johnweldon1993

|dw:1442584881833:dw|

8. johnweldon1993

|dw:1442584923535:dw|

9. anonymous

ohhhhh

10. johnweldon1993

The inscribed angle *According to the Cenntal Angle Theorem* is always equal to HALF the central angle

11. anonymous

what does that mean?

12. johnweldon1993

SO If we look again at that formula I gave you $\large s = r\theta$ S = arc length *What we need r = radius of the circle $$\large \theta$$ = the measure of the central angle in radians

13. anonymous

i've never seen that 0 thing before.

14. johnweldon1993

$$\large \theta$$ = theta = a measure of an angle :)

15. anonymous

oh ok

16. johnweldon1993

yeah lol sorry :D Okay so...lets look at your circle |dw:1442585177036:dw|

17. johnweldon1993

Comparing that to my circle I drew above, it looks like you have the INSCRIBED angle labeled here right? |dw:1442585225131:dw|

18. johnweldon1993

SO...since that formula $\large s = r\theta$ Requires the CENTRAL angle...and we have the inscribed...what would be the central angle?

19. anonymous

|dw:1442585190505:dw|

20. johnweldon1993

Not quite.. So if r = 18 remember And we have 80 degrees (because remember central is always double the inscribed) We have $\large s = 18 \times (80 \times (\frac{\pi}{180}))$ $\large s = 18 \times \frac{4\pi}{9}$ $\large s = ?$ Does that make sense?

21. anonymous

the inscribed angle looks bigger than the central angle why is it only half the central angle?

22. johnweldon1993

It looks bigger?|dw:1442585541996:dw|

23. anonymous

ohhhhh okay i see

24. johnweldon1993

Idk if that helped...or made it more confusing...

25. johnweldon1993

Okay good lol

26. johnweldon1993

So yeah...look back up to my formula up there...Does it make sense? $\large s = r\theta$ $\large s = 18 \times (80 \times \frac{\pi}{180})$

27. anonymous

yes

28. johnweldon1993

Perfect, Also I notice above you had $\large \frac{{\pi}}{360}$ If you want to use 360 on the bottom...make sure you have 2pi on top...because remember 2pi is 360 degrees

29. anonymous

2pi is 360 degrees?

30. johnweldon1993

Indeed |dw:1442585940253:dw|

31. johnweldon1993

Remember a whole circle is 360 degrees right?

32. johnweldon1993

If we travel pi units around the circle...we travel halfway around it...or half of the 360 which is 180

33. johnweldon1993

If we then travel another pi units around....2pi....we have traveled around the whole circle...or 360 degrees

34. anonymous

ohhhhh

35. johnweldon1993

Alright cool, so now that we have that all clear simplify my equation down $\large s = 18 \times (\frac{80\pi}{180})$ $\large s = 18\times (\frac{4\pi}{9})$ $\large s = 2\times 4\pi$

36. anonymous

|dw:1442586054554:dw|

37. johnweldon1993

Where is that 36pi term coming from?

38. anonymous

|dw:1442586190316:dw|

39. anonymous

36 pi is from the diameter

40. anonymous

which is the circumference of the whole circle

41. anonymous

i subtracted the circumference from the central angle

42. anonymous

Is arc ABC the same as arc AC

43. johnweldon1993

Well now the only thing is The want the length of arc ABC |dw:1442586432497:dw|

44. anonymous

|dw:1442586538130:dw|

45. johnweldon1993

So we found that length already...the 8pi By subtracting the 8pi from the whole circumference...we are actually getting |dw:1442586574680:dw|

46. anonymous

Yea i think that's what they wanted

47. anonymous

Is there a reason we have to find the central angle to find the arc length? Couldnt we have found it using the inscribed angle?

48. anonymous

@johnweldon1993