









Remember
from the page about crossed lines 


that
angles A and C are the same size, 


and
angles B and D are the same size ... 





We can
drop a circle over these crossed lines 


so the
center of the circle is right at the cross. 











Just
dropping the circle on this puppy 


doesn't
change the angles. 


The
measure of angle A 


is still
the same as the measure of angle C. 


And the
measure of angle B 


is still
the same as the measure of angle D. 





We put
the center of the circle where the lines crossed. 


That
means, that the piece of the circle out from angle A 


is the
same length as the piece of the circle out from angle C! 











Since the
piece of the circle out from angle A 


is equal
to the piece of the circle out from angle C, 


it should
be no big shock that the piece of the circle 


out from
angle B is equal to the piece of the circle 


out from
angle D! 











This may
seem kind of boring, 


but math
types do lots of stuff with this 





Example: 











The
diameter of the circle is 10 


The
measure of angle D is 40 degrees 


What is
the length of the circle out from angle A? 





Since
angle D is 40, angle B is 40 also ... 











Now we
need to find the measure of angle A ... 





The
angles add up to 360 degrees 


Angle A
is the same as angle C. 





So: 


A
+ 40 + C + 40 = 360



A + A + 80 = 360 


2A + 80 = 360 


2A = 280 


A = 140 











So we
need to know the arc length 


out from
the 140 degree angle on top. 





Way back
when we said that the diameter was 10. 


That
makes the circumference 10 x p 





The arc
on top is 140 of the 360 so: 





Arc
Length = 10p
× 
140 

360 



Arc
Length »
12.217






copyright 2005 Bruce Kirkpatrick 
