Length of Tangent

The word “tangent” literally translates as “to touch.” The Latin word for this is “tangere,” which means “tiger.” We can say that a tangent is a line that intersects a circle exactly at one point on its circumference and never enters the circle’s interior. Tangents are also known as perpendicular lines. There are numerous tangents to a circle. They are parallel to the radius and perpendicular to the axis. Continue reading this article to discover more about tangent meaning and theorems in more detail.

Tangent to a Circle

A tangent is a line that connects two infinitely close points on a circle starting from a point on the circle. In other terms, we can state that Tangents are the lines that cross the circles exactly at the same location on either side of the circle. The point of tangency is the point at which the tangent crosses the circumference of the circle. Tangency is defined as the point at which a tangent runs perpendicular to a radius. This is connected to a number of theorems since it plays a vital role in geometrical constructs and mathematical proofs. We’ll take them one at a time and examine them.

Properties of Tangents

The following points about the properties of tangents

• The tangent line never crosses the circle; instead, it only touches it.

• At the point of tangency, the tangent line is perpendicular to the circle’s radius.

• A chord and tangent form an angle, and the angle formed by the chord and tangent is the same as the angle formed by the tangent inscribed on the opposite side of the chord.

• The tangent segments to a circle from the same external point are equal.

Tangents Formula

The formula for the tangent is given in the following section. Please refer to the following diagram for a detailed explanation of the formula.

Consider the case of a circle whose exterior point is denoted by P. The circle has a tangent at the points A and B when viewed from the outside of the circle. A secant is a straight line that divides a curve into two or more parts by cutting it in half. As a result, the secant PR is drawn, and at Q, R intersects the circle, as shown in the upper diagram of the circle. It is stated in the tangent-secant formula that:

PR/PS = PS/PQ

PS2 is the same as PQ.PR

Point of Tangency

As described by the definition of tangency, this is the single point of a junction where the straight line contacts or intersects with the circle. The point of tangency is represented by the letter P in the diagram above.

Tangent Theorems

On the tangent of a circle, there are two theorems that are very essential. The tangent to radius theorem and the theorem of two tangents are examples of such theorems. Let’s take a closer look at their claims and supporting evidence.

Tangent Radius Theorem: Tangents are defined as the line segment that passes through any point on a circle and is perpendicular to the radius through the point of contact.

Given: A circle S is tangent to a line PL (which passes through the centre of another circle O), and the point of contact is A.

To prove: OA is perpendicular to the tangent PL.

Proof: Point P is located outside of the circle, as evidenced by the diagram. When we join PO, we receive PO > OA (radius of a circle). Except for point A, this condition will apply to every point on the line PL except for that point.

This establishes that the distance between point O and all of the other points on PL is the smallest of all possible distances.

As a result, it has been demonstrated that OA is perpendicular to PL.

Conclusion

When it comes to geometry, a tangent is a line that is drawn from an external point and passes through a certain point on a curve. For instance, when you ride a bicycle, you will see that every point on the circle of the wheel will be at a right angle to the road.