SOLUTION: if an arc with length of 12 phi is 3/4 the circumference of a circle. what is the shortest distance between the end points of the arc?

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Question 353183: if an arc with length of 12 phi is 3/4 the circumference of a circle. what is the shortest distance between the end points of the arc?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

The circumference of a circle is,
C=pi%2AD
pi%2AD=12%2Api
D=12
If we looked at the circle on a coordinate system, the one endpoint would be at (R,0) and the other would be at (0,R), where R is the radius of the circle.
The shortest distance between two points in Euclidean geometry is a straight line.
The two points and the origin also desribe an isoceles right triangle with equals length sides of R.
You can use the Pythaogorean theorem to find the hypotenuse.
R%5E2%2BR%5E2=H%5E2
H%5E2=2R%5E2
H=sqrt%282%29%2AR
H=sqrt%282%29%2A%28D%2F2%29
H=sqrt%282%29%2A6
highlight%28H=6%2Asqrt%282%29%29