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Figure 1: Segment of a Circle Derivation. In fig. 1, if ∠AOB = θ (in degrees), then the area of the sector AOBC (A sector AOBC) is given by the formula; (A sector AOBC) = θ/360° × πr 2. Let the area of ΔAOB be A ΔAOB. So, the area of the segment ABC (A segment ABC) is given by. (A segment ABC) = (A sector AOBC) – A ΔAOB.
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Example 3: Find the area of the major segment of a circle if the area of the corresponding minor segment is 62 sq. units and the radius is 14 units. Use π = 22/7. Solution: Area of the major segment = area of the circle - area of the minor Segment. = πr 2 − 62. = (22/7) × 14 × 14 − 62. = 554 sq. units.
This is the reasoning: A circle has an angle of 2 π and an Area of: πr2. A Sector has an angle of θ instead of 2 π so its Area is : θ 2π × πr2. Which can be simplified to: θ 2 × r2. Area of Sector = θ 2 × r 2 (when θ is in radians) Area of Sector = θ × π 360 × r 2 (when θ is in degrees)
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May 24, 2024 · Formula given radius and central angle. A segment = 0.5 × r² × (α – sin(α)) Where does this formula come from? You can look at the segment area as the difference between the area of a sector and the area of an isosceles triangle formed by the two radii: A segment = A sector - A triangle. Knowing the sector area formula:
Secants, Tangents - MathBitsNotebook (Geo) If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other. If two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the ...
Jan 18, 2024 · To find the length of a line segment with endpoints: Use the distance formula: d = √ [ (x₂ - x₁)² + (y₂ - y₁)²] Replace the values for the coordinates of the endpoints, (x₁, y₁) and (x₂, y₂). Perform the calculations to get the value of the length of the line segment.
Aug 3, 2023 · Area of a Segment of a Circle = θ/360° × πr 2 – ½ r 2 sinC. Factoring by 1/2r 2 we get, Area (A) of a Segment of a Circle = ½ × r2 × (πθ /180 – sin θ) Thus, if the radius is known and the central angle of the segment is given in degrees, the formula to find the area of a segment is given below. Segment of a Circle Formula.
