According to geometry, a straight line that just touches the curve at that point is called the tangent line to a plane curve at that particular location. Leibniz found out that a line connecting two infinitely close points on a curve. Space curves and curves in n-dimensional Euclidean space have a similar definition. The tangent line is “moving in the same direction” as the curve when it passes through the point where the tangent line and the curve meet, called the point of tangency, and is thus the best straight-line approximation to the curve at that moment.

The graph of the affine function that best approximates the original function at a particular location is known as a tangent line approximation, which is the tangent line to a point on a differentiable curve.

Likewise, the tangent plane to a particular point on a surface is the plane that “just touches” the surface at that point. Tangent space is a generalization of the concept of a tangent, which is one of the most fundamental concepts in differential geometry.

The word tangent comes from the Latin word Tangere, which literally means “to touch.”

**Point of Tangency**

The only point of intersection where the straight line contacts or intersects the circle is known as the point of tangency.

**Properties of Tangent**

The tangent has two key characteristics:-

- Only one point on a curve is touched by a tangent.
- A tangent is a line that never passes through the center of the circle.
- The tangent makes a right angle contact with the radius of the circle.

Aside from the qualities described above, a tangent to the circle is related to mathematical theorems that are used while doing major calculations in geometry.

**Applications on Tangent**

Suppose a person is close to the corner of the road, suddenly the wheels of the car come in contact with a viscous substance which was there at the corner( oil, ice, water, or loose gravel), the car will begin to slide and it will continue to slide in a direction which is opposite to the direction of the curve.

Similarly, if we hold a ball in our hands and start swinging it in a circular manner, a time will come when we will lose our grip and at that time, just before releasing the ball will fly out in a tangent to the circle of motion. You can refer to the Cuemath website to understand the topic in a fun and easy manner.

**Area of a Circle – Introduction**

A circle’s area is the amount of space it takes up in a two-dimensional plane. The area of a circle, on the other hand, is the space occupied within the boundary/circumference of a circle. The formula A = (pie*r)/2, where r is the radius of the circle, and this formula is used to compute the area of a circle. The square unit, such as m2, cm2, in2, and so on, is the unit of area. In square units, the area of a circle is equal to r2 or d2/4, where (Pi) = 22/7 or 3.14. The circumference to diameter ratio of any circle is Pi (). It’s a mathematical constant that’s unique.

The area of a circle formula can be used to calculate the area of a circular field or plot. If you have a circular table, for example, the area formula will tell you how much fabric you’ll need to completely cover it. The boundary length, or circumference of the circle, can alternatively be determined using the area formula. Is volume present in a circle? No, the volume of a circle is zero. There is no volume in a circle because it is a two-dimensional shape. The perimeter/circumference of a circle is the only thing it has.