Let us use this logic to derive the formulas to find the area of a segment of a circle. Note that this is the area of the minor segment. Usually, a segment of a circle refers to a minor segment. Note: To find the area of the major segment of a circle, we just subtract the corresponding area of the minor segment from the total area of the circle.
Let us consider the minor segment of the above circle that is made by the chord PQ of a circle of radius 'r' that is centered at 'O'. We know that every arc of a circle subtends an angle at the center which is referred to as the central angle of the arc.
Also, we know that the area of the sector OPQ is:. We know that the segment of a circle is made up of an arc and a chord of the circle. Consider the same segment as in the above figure. It states that angles formed in the same segment of a circle are always equal. This theorem states that the angle formed by the tangent and the chord at the point of contact is equal to the angle formed in the alternate segment on the circumference of the circle through the endpoints of the chord.
Example 1: In a pizza slice, if the central angle is 60 degrees and the length of its radius is 4 units, then find the area of the segment formed if we remove the triangle part out of the pizza slice. Round your answer to two decimals. Example 2: If the area of a sector is sq. Example 3: Find the area of the major segment of a circle if the area of the corresponding minor segment is 62 sq. There are two types of segments, one is a minor segment made by a minor arc and the other is a major segment made by a major arc.
A chord of a circle is a line segment that joins any two points on its circumference whereas a segment is a region bounded by a chord and an arc of the circle. An arc is a portion of a circle's circumference whereas a segment of a circle is a region bounded by an arc and a chord of the circle. In a plane 2D Geometry , a line segment joining two points on a curve is called a chord. The term is often used to describe a line segment with its ends lying on the circumference of a circle.
But it can also describe line segments drawn on ellipses and conic sections. Among many others, chords of a circle exhibits following properties:. A secant line is a line passing through two points of a curved line. The minor segment is the region bounded by the chord and the minor arc intercepted by the chord. The major segment is the region bounded by the chord and the major arc intercepted by the chord.
Use the information given in the diagram to prove that the angles in the same segment of a circle are equal. If there are rocks near the shore, then boats are informed by the chart map to keep the angle subtended by two land marks, A and B , smaller than the given danger angle. All positions on the same arc of a circle give the same angle for scoring a goal in soccer. Note that the distance of the shot changes but the angle of possible shots remains constant.
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