The chord ST of a circle is equal to the radius, r, of the circle. Find the length of arc ST.
Question 1 Report
The chord ST of a circle is equal to the radius, r, of the circle. Find the length of arc ST.
Answer Details
In a circle, the length of an arc is proportional to the angle it subtends at the center of the circle. Since ST is a chord and its length is equal to the radius of the circle, then angle SOT, where O is the center of the circle, is 60 degrees (because it subtends an equilateral triangle).
Therefore, the length of arc ST is 1/6 of the circumference of the circle (because 60 degrees is 1/6 of a full revolution, which is 360 degrees). The circumference of the circle is 2πr, so the length of arc ST is:
Length of arc ST = 1/6 * 2πr = πr/3
Hence, the answer is option D: πr/3.
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