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Oct 24, 2024 · You can calculate the segment area in three steps: Determine the radius of the circle. Calculate the central angle. Apply the segment area formula: 0.5 × r² × (α – sin(α))
Circular segment - is an area of a "cut off" circle from the rest of the circle by a secant (chord). If you know the radius and the angle, you may use the following formulas to calculate the remaining segment values: If you don't know the radius and the angle, you can calculate the segment parameters by the chord length and the segment height:
- Segment of A Circle Definition
- Types of Segments in A Circle
- Area of A Segment of A Circle Formula
- Theorems on Segment of A Circle
- Practice Questions
A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord’s endpoints. In other words, a circular segment is a region of a circle which is created by breaking apart from the rest of the circle through a secant or a chord. We can also define segments as the parts that are divided by the circl...
According to the definition, the part of the circular region which is enclosed between a chord and corresponding arc is known as a segment of the circle. There are two classifications of segments in a circle, namely the major segment and the minor segment. The segment having a larger area is known as the major segment and the segment having a small...
The formula to find segment area can be either in terms of radians or in terms of degree. The formulas for a circle’s segment are as follows:
There are two main theorems based on a circle’s segments which are: 1. Alternate Segment Theorem 2. Angle in the Same Segment Theorem 3. Alternate Angle Theorem
A chord of a circle of radius 14 cm makes a right angle at the centre. Find the areas of the major and minor segments of the circles formed.Find the area of both the segments cut off by a chord of length 10 cm of a circle whose radius is 5√2 cm.A chord of a circle of radius 30 cm makes an angle of 60° at the centre of the circle. Find the areas of the minor and major segments.- 8 min
A segment of a circle is the region that is bounded by an arc and a chord of the circle. Learn the process of finding the area of a segment of a circle along with a few solved examples and practice questions.
Area of a circular segment and a formula to calculate it from the central angle and radius. Including a calculator.
The area of a segment is the area of the sector minus the area of the triangle. If $\theta$ is the angle of the arc (in radians), the area of the sector is $\frac12\theta\cdot R^2$, and the area of the triangle is $2\frac12R\sin\frac\theta2R\cos\frac\theta2=\frac12R^2\sin\theta$. The area of the segment is therfor: $A=\frac12R^2(\theta-\sin ...
The Formula for the Area of a Circular Segment. The area \( A \) of a circular segment can be found using the formula: \[ A = r^2 \cdot \left( \frac{\theta \cdot \pi}{360^\circ} - \frac{\sin(\theta)}{2} \right) \] Where: - \( r \) is the radius of the circle. - \( \theta \) is the segment angle in degrees. Explaining the Formula
