CBSE 10
CBSE 10 Geometry: The Secrets of the Perfect Symmetry of Circles (Formulas Revealed)
May 16, 2024
Aha
Language
English
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If you are studying geometry, then you must learn about circles. In this article, we will cover everything you need to know about circles, including definitions, formulas, and solved examples.
A circle is a closed shape that is perfectly round. It has no corners or edges. In geometry, a circle is defined as a set of points that are equidistant from a fixed point, called the center.
Circles can be found in many objects in our daily life. A wheel, a clock, a pizza, and a frisbee are all examples of objects that are circular in shape.
Drawing a circle is easy. All you need is a compass and a straight edge. Here are the steps to draw a circle:
A circle has several parts, including the center, radius, diameter, chord, sector, and segment.
The center of a circle is the fixed point that is equidistant from all points on the circle. It is denoted by the letter "O". The center is the point around which the rest of the circle is constructed, and it is often used as a reference point for other measurements, such as the radius and diameter.
The radius of a circle is the distance from the center of the circle to any point on the circle. It is denoted by the letter "r".
The diameter of a circle is the distance across the circle, passing through the center. It is twice the length of the radius. It is denoted by the letter "d".
A chord of a circle is a straight line segment that connects two points on the circle. The diameter of a circle is a special type of chord that passes through the center of the circle. The length of a chord can be calculated using the distance formula or the Pythagorean theorem.
A sector of a circle is a region bounded by two radii of the circle and an arc of the circle. It is similar to a slice of pizza or a piece of pie. The two radii that bound the sector are called the initial radius and terminal radius, and the arc that bounds the sector is called the sector arc.
Sectors are often used in real-world applications, such as calculating the area of a slice of pizza or the angle of view of a camera lens.
A segment of a circle is a region bounded by a chord and an arc of the circle. It is similar to a slice of pizza or a piece of pie, but it does not include the center of the circle. The chord that bounds the segment is called the base of the segment, and the arc that bounds the segment is called the segment arc.
Segments are often used in real-world applications, such as calculating the area of a pizza slice or the angle of view of a camera lens.
Here are some important formulas related to circles:
Here are some important properties of circles:
Find the circumference of a circle with radius 5 cm.
✅ Solution: Circumference of the circle = 2πr = 2π * 5 = 10π cm.
Find the area of a circle with diameter 6 cm.
✅ Solution:
1. Radius of the circle = 6 / 2 = 3 cm.
2. Area of the circle = πr² = π * 3² = 9π cm².
A circle is a closed shape that is perfectly round. It has no corners or edges. In geometry, a circle is defined as a set of points that are equidistant from a fixed point, called the center.
A circle has several parts, including the center, radius, diameter, chord, sector, and segment.
Here are some important formulas related to circles:
Circles are an important part of geometry, and understanding them is crucial for solving many mathematical problems. We hope this article has been helpful in teaching you everything you need to know about circles. If you need further assistance, visit Aha AI for more resources.
