Circles

Circle is a collection of all points in a plane, which are equidistant from a central point. There can be three distinct possibilities arising between a line and circle given on the same plane. 1. No common point 2. Two common points 3. One common point When the line intersects the circle they have two common points. In this case the line is called a secant of the circle. When the line just touches the circle they have one common point. In this case the line is called a tangent to the circle. The common point is called the point of contact. The tangent to a circle is a special case of the secant when both the end points of its corresponding chord coincide. Theorem: The tangent at any point of a circle is perpendicular to the radius through the point of contact. Number of Tangents from a Point on a Circle • It is not possible to get any tangent when the point is inside the circle. • Only one tangent can be drawn from a point on the circle. • Only two tangents can be drawn from a point outside the circle. Theorem: The lengths of tangents drawn from an external point to a circle are equal.

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