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

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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

Mathematics
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|dw:1442538379561:dw|
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?
18

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what do you mean by the angle in radian?
Can you tell me what they mean when they say "An inscribed angle is aways half the central angel."
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
|dw:1442584881833:dw|
|dw:1442584923535:dw|
ohhhhh
The inscribed angle *According to the Cenntal Angle Theorem* is always equal to HALF the central angle
what does that mean?
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
i've never seen that 0 thing before.
\(\large \theta\) = theta = a measure of an angle :)
oh ok
yeah lol sorry :D Okay so...lets look at your circle |dw:1442585177036:dw|
Comparing that to my circle I drew above, it looks like you have the INSCRIBED angle labeled here right? |dw:1442585225131:dw|
SO...since that formula \[\large s = r\theta\] Requires the CENTRAL angle...and we have the inscribed...what would be the central angle?
|dw:1442585190505:dw|
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?
the inscribed angle looks bigger than the central angle why is it only half the central angle?
It looks bigger?|dw:1442585541996:dw|
ohhhhh okay i see
Idk if that helped...or made it more confusing...
Okay good lol
So yeah...look back up to my formula up there...Does it make sense? \[\large s = r\theta\] \[\large s = 18 \times (80 \times \frac{\pi}{180})\]
yes
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
2pi is 360 degrees?
Indeed |dw:1442585940253:dw|
Remember a whole circle is 360 degrees right?
If we travel pi units around the circle...we travel halfway around it...or half of the 360 which is 180
If we then travel another pi units around....2pi....we have traveled around the whole circle...or 360 degrees
ohhhhh
Alright cool, so now that we have that all clear simplify my equation down \[\large s = 18 \times (\frac{80\pi}{180})\] \[\large s = 18\times (\frac{4\pi}{9})\] \[\large s = 2\times 4\pi\]
|dw:1442586054554:dw|
Where is that 36pi term coming from?
|dw:1442586190316:dw|
36 pi is from the diameter
which is the circumference of the whole circle
i subtracted the circumference from the central angle
Is arc ABC the same as arc AC
Well now the only thing is The want the length of arc ABC |dw:1442586432497:dw|
|dw:1442586538130:dw|
So we found that length already...the 8pi By subtracting the 8pi from the whole circumference...we are actually getting |dw:1442586574680:dw|
Yea i think that's what they wanted
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?

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