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How To Find the Area of a Segment of a Circle? Here are the steps to find the area of a segment of a circle. Identify the radius of the circle and label it 'r'. Identify the central angle made by the arc of the segment and label it 'θ'. Find the area of the triangle using the formula (1/2) r 2 sin θ.
- Subtended
An arc of a circle is any part of the circumference. The...
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Circles. A circle is a 2-dimensional closed shape that has a...
- Chord
A chord of a circle is any line segment joining two points...
- Sector
The region OAPB is called the minor sector and the region...
- Tangent
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- Circumference
If you know the diameter 'd' of a circle, then you can...
- Diameter
When the area of the circle is given, then diameter =...
- Area
The area of any shape is the number of unit squares that can...
- Subtended
- 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
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))
Aug 3, 2023 · Find the area of the major segment of a circle if the area of the corresponding minor segment is 88 m 2 and the radius is 22 m. Use π = 3.141.
To find the area of a segment of a circle, you can use the formula for the area of a triangle and the formula for the area of a sector. You subtract the area of the triangle from the area of the sector.
Area of Major Segment = Area of Circle – Area of Minor Segment. Hence, Area of Major Segment = πr2 – ( θ 360 πr2 – 1 2 r2sinθ) Example : A chord 10 cm long is drawn in a circle whose radius is √50 cm. Find the area of segments. Solution : Radius of the circle = √50 cm.
Geometrically, the area of a major segment with central angle 𝜃 ∘ is the sum of the area of the major sector, shown in blue on the figure below, and a triangle, shown in orange. Note that the angle of the major sector is 𝜃 ∘ , but the angle in the triangle is ( 3 6 0 − 𝜃 ) ∘ .
