Posted by Dixie on .
In a circle , the radius is 68 units and a chord of the circle is 120 units.
Part A)How far is the chord from the center?
Part B)Find the measure of the arc created by the chord.
A) Let x be the distance of the chord from the center. Draw a line from the center of the chord to the center of the circle. This forms a right triangle with a radius and half the chord.
x^2 + 60^2 = r^2 = 4624
x^2 = 1024
x = 32
B) The angle subtended by the chord is 2 arcsin 60/68 = 123.85 degrees = 2.162 radians
Multiply that by the radius to get the arc length, 147.0 units.. a bit longer than the chord length, as you would expect.