Circle
A circle is a shape that is formed by all the points in a plane that are equidistant from a fixed point called the center
A circle is a shape that is formed by all the points in a plane that are equidistant from a fixed point called the center. It is a closed curve and is defined by its radius and diameter.
– Radius: The radius of a circle is the distance from the center of the circle to any point on its circumference. It is usually denoted by the letter ‘r’.
– Diameter: The diameter of a circle is the distance across the circle, passing through the center. It is equal to twice the radius. Mathematically, it is represented as ‘d = 2r’.
– Circumference: The circumference of a circle is the distance around its edge or boundary. It is calculated using the formula ‘C = 2πr’, where π (pi) is a mathematical constant approximately equal to 3.14159.
– Area: The area of a circle is the measure of the region enclosed by the circle. It is calculated using the formula ‘A = πr^2’, where ‘r’ is the radius of the circle.
Properties of a circle:
1. All points on the circumference of a circle are equidistant from the center.
2. The diameter is the longest chord that can be drawn in a circle.
3. The radius perpendicular to a chord bisects the chord.
4. The angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the circumference.
5. The length of an arc is proportional to the angle subtended by it at the center.
Example: Let’s say we have a circle with a radius of 5 cm.
– Diameter: The diameter would be 2 times the radius, so it would be 2 * 5 cm = 10 cm.
– Circumference: Using the formula C = 2πr, we can calculate the circumference as C = 2 * 3.14159 * 5 cm ≈ 31.4159 cm.
– Area: Using the formula A = πr^2, we can calculate the area as A = 3.14159 * (5 cm)^2 ≈ 78.53975 cm^2.
Remember, these formulas and properties can be useful when solving various problems related to circles in geometry or trigonometry.
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