Arc Radius
Using the intersecting chords theorem (also known as power of a point or secant tangent theorem) it is possible to calculate the radius of a circle given the height and the width of an arc:
Consider the chord with the same end-points as the arc. Its perpendicular bisector is another chord, which is a diameter of the circle. The length of the first chord is and it is divided by the bisector into two equal halves, each with length The total length of the diameter is and it is divided into two parts by the first chord. The length of one part is the height of the arc, and the other part is the remainder of the diameter, with length Applying the intersecting chords theorem to these two chords produces:
whence:
so:
Read more about this topic: Arc (geometry)
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“You say that you are my judge; I do not know if you are; but take good heed not to judge me ill, because you would put yourself in great peril.”
—Joan Of Arc (c.1412–1431)