65 (number)

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In geometry, a circular segment (symbol: ) is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord.

Formulas

A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area).

Let R be the radius of the circle, θ is the central angle in radians, α is the central angle in degrees, c the chord length, s the arc length, h the height of the segment, and d the height of the triangular portion.

Area

The area of the circular segment is equal to the area of the circular sector minus the area of the triangular portion.

Area of Segment = ½ × (θ - sin θ) × R² (when angle is in radians)

Area of Segment = ½ × ( (α × π/180) - sin α) × R² (when angle is in degrees)

See also

External links



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