The chord will create a central angle in the circle. To calculate its measure, you can use the cos formula in the right triangle that is formed by the radius, the half-chord, and the segment connecting the center of the circle with the instrument point.
In this case, the radius (r) is 10 cm, and the distance from the center to the chord (d) is 4 cm.
Use the cos formula to find the measure of the angle.
cos(A) = adj/hyp = d/r = 4/10 = 0.4
A = cos^-1(0.4) ≈ 66.42°
Since the chord cuts off two of these angles in the circle, the central angle for the arc is 2 * 66.42° = 132.84°.
The length of an arc (s) on a circle is s = rθ, where θ is the central angle in radians.
To convert the angle to radians, multiply the degree measure by π/180, which yields 132.84° * π/180 = 2.318 radians.
So, the length of the minor arc is s = 10 cm * 2.318 rad ≈ 23.18 cm.
Remember this process gives you the length of the minor arc, which is the shorter arc between the two points where the chord intersects the circle.
In a circle of radius 10cm , A chord is drawn so that it is 4cm distant from the centre. Calculate the length of the minor arc cut off by the chord.
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