Have you ever done or seen fencing around the garden or some road due to some law and order situation? The police will not allow you to go closer to the fence and some might get a chance to touch the fence and walk away too. If they walk in a straight line then they are following a tangent path for the shape made inside the fencing.
That is a definition of a tangent, a line that touches the shape at any one point and moves away. And that is what the Latin word “tangent” means, “to touch.”
Properties of a Tangent
- A tangent can touch a circle at one point of the circle.
- Tangent can never cross a circle, which means it cannot pass through the circle.
- A tangent can never intersect the circle at two points.
- A tangent line is perpendicular to the radius of a circle.
Can the Two Circles be Tangent?
Yes, it can be when two circles are tangent and they are touching each other at exactly one point. As it says, according to the definition of a tangent, which touches the circle at exactly one point.
Circles and Tangents
In our day-to-day real-life situations, we have seen two lines intersect at a point or do not intersect in a plane. For example, two parallel lines in a railway track do not intersect. Whereas, grills in a window intersect.
Examples of Tangents to Circles
- Have you ever wondered that when a cycle moves along a road, the road becomes the tangent at each point when the wheel rolls on it.
- Have you ever thought that when a stone is tied at one end of a string and it’s rotated from the other end then the stone will describe a circle? When we suddenly stop the motion, the stone will go in a direction tangential to the circular motion.
- Another example of a tangent of a circle is the abstract composition of a yellow ball and curb placed tangentially with the projection of spherical shadow on a stone background.
Area of a Circle
The area of a circle is the space that is occupied by the circle in a two-dimensional plane. The circle is a critical geometric figure which is present across many areas such as construction, engineering, and many more. While solving problems related to circles in geometry requires being able to derive the area of a circle.
Examples of Circles
- Camera lenses
- Pizzas
- Tires
- Ferris wheels
- Rings
- Steering wheels
- Cakes
- Pies
- Buttons
- Satellite’s orbit around the Earth
Circle in Daily Life
Look at the shapes all around us. An object with a circular face such as a dining plate, a pop can, a traffic cone, or a circular flower bed in a garden is all built or prepared to keep the concept of the area of a circle in mind.
Main objects where the area of a circle are used:
- The volume and surface area of a cylinder
- Surface area and volume of a cone
- Surface area and volume of a sphere
Examples of Circular-Shaped Objects
- Dishes – Have you ever noticed that the dishes being used to serve food are circular in shape. A dish or a plate is the most common example of circular-shaped objects used in everyday life.
- Hub of the fan – If you have ever observed the structure of the hub, you can easily observe the circle geometric figure in the wings of a fan that are connected to a hub.
- Ornaments – A number of ornaments that we wear are also in a circular shape. For example rings, bracelets, earrings, bangles all constitute a perfect example of circle-shaped objects.
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