Question

Geometry about circle and tangent

Answer 1

Tangent to a circle is a line that touches the circle at one point, which is known as Tangency. At the point of Tangency, Tangent to a circle is always perpendicular to the radius. Let us learn more about tangents in this chapter.Tangent to a Circle

The line that joins two infinitely close points from a point on the circle is a Tangent. In other words, we can say that the lines that intersect the circles exactly in one single point are Tangents. Point of tangency is the point where the tangent touches the circle. At the point of tangency, a tangent is perpendicular to the radius. Several theorems are related to this because it plays a significant role in geometrical constructions and proofs. We will look at them one by one.



[Source: Illustrative Mathematics]

Tangents Formula

The formula for the tangent is given below. For the description of formula, please look at the following diagram.



[Source: Jim Wilson at UGA]

Here,  we consider a circle where P is the exterior point. From that exterior point, the circle has the tangent at a points A and B. A straight line which cuts curve into two or more parts is known as a secant. So, here secant is PR is drawn and at Q, R intersects the circle as shown in the upper diagram. The formula for tangent-secant states that:

PR/PS = PS/PQ

PS2 = PQ.PR