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Current time:0:00Total duration:3:45

Circle theorems — Harder example

Video transcript

a circle has a circumference of 10 PI feet an arc X in the circle has a central angle of 260 degrees what is the length of X so let's just visualize what's going on here so we have a circle I can't draw a circle that well but you get the point so that's our circle is this is the center of our circle it has a circumference of ten pi feet so if you were to go all the way around the circle this it has a circumference of 10 pi 10 PI feet now you have an arc X you have an arc X in the circle that has a central angle of 260 degrees so let's think about so 260 degrees so if you go straight up that's that would see if you go this far be 90 degrees 180 degrees if you were to go all the way here you get to 270 so it's gonna be right around and we just approximating right around there so that would be a central angle of 260 260 degrees and this is the arc this is arc let me do this in a different color let me do it in purple so this is arc X right over here and we want to figure out its length well think about it this way its central angle is 260 degrees what's the central angle of the circumference well the circumference is going all the way around so if you're going all the way around that is 360 degrees 360 degrees so the fraction that this that arc X is the length of X's of the entire circumference that's going to be the same fraction that its central angle is of 360 degrees so once again the entire circumference is 10 PI feet 10 PI feet that's the circumference now the fraction of that circumference that's going to be arc X that's going to be the fraction that 200 that's going to be the same fraction of the central angle of that arc relative to the central angle if you were to go all the way around which would be 360 degrees so it'll be 260 360 it's of their circumference so what's that going to be well let's see we can simplify this a little bit we could if we divide the numerator the denominator by 10 10 divided by 10 is 1 and let me let me make it actually let me just write it this way so we could write this as 2 the 2260 times 10 pi is going to be 2600 pi over 360 over 3 and 60 and now we just need a simplify if we divide the numerator and the denominator by 10 this is gonna be 260 this is going to be 36 if we divide the numerator and the denominator by let's see it seems like they are both divisible by 4 260 divided by 4 is going to be let's see 200 divided by 4 is 50 60 divided by 4 is 15 15 plus it's gonna be 65 so let me just a different color this is going to be 65 and 36 divided by 4 is 9 and just so you see I didn't you know I was trying to do in my head and it's good to get some practice doing that but all I did is divided both the numerator and the denominator by 4 4 goes into 260 four goes into 26 6 times 6 times 4 is 24 subtract you get a to bring down that 0 4 goes into 20 5 times 5 times 4 is 20 so that's all I did there so it's 65 PI over 9 and it looks like that's a lot of simplified as I'm gonna get and that's nice because that's one of the choices right over here