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 chords of the circle, and the vertical one passes through the center, bisecting 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:
Combining terms
Dividing both sides by H

Now, the diameter of the circle is equal to b+c, and b is the height H, so The radius is half the diameter, so dividing through by 2:

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- Area of a circle
- Concentric circles
- Annulus
- Area of an annulus
- Sector of a circle
- Area of a circle sector
- Segment of a circle
- Area of a circle segment (given central angle)
- Area of a circle segment (given segment height)

- Basic Equation of a Circle (Center at origin)
- General Equation of a Circle (Center anywhere)
- Parametric Equation of a Circle

- Arc
- Arc length
- Arc angle measure
- Adjacent arcs
- Major/minor arcs
- Intercepted Arc
- Sector of a circle
- Radius of an arc or segment, given height/width
- Sagitta - height of an arc or segment

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