Arc radius formula derivation
This page describes how to derive the forumula for the
radius of an arc given the arc's width W, and height H.
The arc radius equation is a use of the
intersecting chord theorem.
In the figure on the right the two lines are
of the circle, and the vertical one passes through the center,
the other chord.
The blue segment is the arc whose radius we are finding. Its width is 2a, and height b.
Recall from the intersecting chord theorem that
Since a is half the arc's width W, and b is its height H:
Dividing both sides by H
of the circle is equal to b+c, and b is the height H, so
is half the diameter, so dividing through by 2:
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Other circle topics
Equations of a circle
Angles in a circle
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