The length of an arc is given by the formula s = θr, where θ is the angle (in radians) subtended by the arc at the center of the circle and r is the radius of the circle.
In this case, since chord ST is equal to the radius r, we can consider the triangle STR formed by the chord and two radii.
Since a triangle in a circle with one side equal to the radius is an equilateral triangle, all angles of triangle STR are equal to 60 degrees (or π/3 radians).
Thus, the length of arc ST is s = θr = (π/3)r.
Therefore, the answer is D. πr/3.
The chord ST of a circle is equal to the radius, r, of the circle. Find the length of arc ST.
A. πr/6
B. πr/2
C. πr/12
D. πr/3
1 answer