What do tangent and secant mean

The tangent line represents the instantaneous rate of change of the function at that one point. Answer: The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.

A circle can have two parallel tangents at the most. Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

In geometry, a secant of a curve is a line that intersects the curve at a minimum of two distinct points. Two Secants. Interactive Applet. Practice Problems. In this diagram, the red line is a tangent, how long is it? Length of tangent. Popular pages mathwarehouse. This property of tangent to a circle is established in the following theorem:. Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

But, the shortest distance between a point and a line is the perpendicular distance from the point to the line. Theorem 2: Converse of theorem 1 : A line drawn through the end of a radius and perpendicular to it is a tangent to the circle. Proof: We know that the perpendicular distance between points to lines is the shortest distance between them. The line perpendicular to a tangent at the point of contact is known as the normal to the circle at the point of control.

Suppose a tangent segment and the secant segment are drawn to a circle from an exterior point. Here, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment. Find the radius of the circle.

In the given article, we have discussed the tangent and secant properties of a circle followed by the secant of a circle. Then we talked about intersecting secant-tangent theorem, which includes Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact, and Theorem 2: Converse of theorem 1 : A line drawn through the end of a radius and perpendicular to it is a tangent to the circle.

It's important, therefore, to know exactly how and where the plane of a map projection contacts the earth's surface since these tangents or secants are lines of zero distortion on the map. Now examine a globe or imagine the earth as an object before you. You could look at it from different points of view: straight on, sideways, from above, or from some odd angle. In a map projection, these points of view are called aspects. Some map projections contact the earth's surface along a point or line, called a tangent, while other map projections contact the earth's surface along two lines, called secants.