area of a Circle Corner formula |
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| \( A \;=\; \dfrac{ a\cdot b - r \cdot L + c \cdot (r - h) }{ 2 }\) | ||
| Symbol | English | Metric |
| \( A \) = area | \(ft^2\) | \(m^2\) |
| \( L \) = arc length | \(ft\) | \(m\) |
| \( c \) = chord length | \(ft\) | \(m\) |
| \( a, b \) = edge | \(ft\) | \(m\) |
| \( r \) = radius | \(ft\) | \(m\) |
| \( h \) = segment height | \(ft\) | \(m\) |
Circle corner (a two-dimensional figure) is a right triangle having acute vertices on a circle with the hypotenuse outside the circle.
Chord is a line segment on the interior of a circle.
Segment of a circle is an interior part of a circle bound by a chord and an arc.
Arc Length of a Circle Corner formula |
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| \( L \;=\; r \cdot \Delta \) | ||
| Symbol | English | Metric |
| \( L \) = arc length | \(ft\) | \(m\) |
| \( \Delta \) = angle | \(deg\) | \(rad\) |
| \( r \) = radius | \(ft\) | \(m\) |
Chord Length of a Circle Corner formula |
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| \( c \;=\; a^2 \cdot b^2 \) | ||
| Symbol | English | Metric |
| \( c \) = chord length | \(ft\) | \(m\) |
| \( a, b \) = edge | \(ft\) | \(m\) |
Height of a Circle Corner formula |
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| \( h \;=\; r \cdot \left( 1 - cos \left( \dfrac{\Delta}{2} \right) \right) \) | ||
| Symbol | English | Metric |
| \( h \) = segment height | \(ft\) | \(m\) |
| \( \Delta \) = segment angle | \(deg\) | \(rad\) |
| \( r \) = radius | \(ft\) | \(m\) |
Perimeter of a Circle Corner formula |
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| \( p \;=\; a + b + L \) | ||
| Symbol | English | Metric |
| \( p \) = perimeter | \(ft\) | \(m\) |
| \( L \) = arc length | \(ft\) | \(m\) |
| \( a, b \) = edge | \(ft\) | \(m\) |
Segment Angle of a Circle Corner formula |
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| \( \Delta \;=\; arccos \left( \dfrac{2\cdot r^2 - c^2 }{ 2\cdot r^2 } \right)\) | ||
| Symbol | English | Metric |
| \( \Delta \) = segment angle | \(deg\) | \(rad\) |
| \( c \) = chord length | \(ft\) | \(m\) |
| \( r \) = radius | \(ft\) | \(m\) |