Given a circle with diameter d, is there a way to find the length of the chord f that cuts off an arc of length l?I am trying to understand the relationships between chords and arcs etc, and this concept came up - is there a general formula for it?(And before I get shut down for this being a homework question, it is not. The concept came up in independent study.)

Question

Given a circle with diameter   d, is there a way to find the length of the chord f that cuts off an arc of length   l?I am trying to understand the relationships between chords and arcs etc, and this concept came up - is there a general formula for it?(And before I get shut down for this being a homework question, it is not. The concept came up in independent study.)

kpgt1z · Accepted Answer

The angle of the corresponding circular sector is             2      l        d  . If you trace a line from the center through the midpoint of the chord and two more lines from the center to the chord&#039;s endpoints, you will have two right triangles. It follows from basic trigonometry that:      f    2    =      d    2    sin  ⁡      (          l      d        )  and therefore  f  =  d  sin  ⁡      (          l      d        )

Given a circle with diameter d , is there a way to find the length of the chord f that cuts off a

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