A circle has a center at (7 ,5 ) and passes through (4 ,3 ). What is the length of an arc covering pi /4 radians on the circle?

1 Answer
Oscar L.
Mar 6, 2016

(\sqrt{13})(\pi/4), about 2.832 units.

Explanation:

First figure out the radius of the circle. If (x_1, y_1) is the center and the circle passes through (x_2, y_2) then

r^2=(x_1-x_2)^2+(y_1-y_2)^2=(7-4)^2+(5-3)^2=13

So r=\sqrt(13).

Now a radian is the amount of arc whose length equals the radius, about 57.2958 degrees. So when you have the arc in radians its length is the number of radians times the radius.

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