Today our topic of discussion is Secant and Tangent of the circle.
Secant and Tangent of the circle
Secant and Tangent of the circle
Consider the relative position of a circle and a straight line in the plane. Three possible situations of the following given figures may arise in such a case:
1) The circle and the straight line have no common points
2) The straight line has cut the circle at two points
3) The straight line has touched the circle at a point.
A circle and a straight line in a plane may at best have two points of intersection. If a circle and a straight line in a plane have two points of intersection, the straight line is called a secant to the circle and if the point of intersection is one and only one.
The straight line is called a tangent to the circle. In the latter case, the common point is called the point of contact of the tangent. In the above figure, the relative position of a circle and a straight line is shown.
In figure,
(i) the circle and the straight line PQ have no common point; in figure
(ii) the line PQ is a secant, since it intersects the circle at two points A and B and in figure
(iii) the line PQ has touched the circle at A. PQ is a tangent to the circle and A is the point of contact of the tangent.
Remarks: All the points between two points of intersection of every secant of the circle lie interior of the circle.
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