Circles and Tangents from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
The concept of Circles and Tangents is an important topic in geometry. A circle is a set of all points in a plane that are at a fixed distance from a given point called the center. A tangent is a line that touches the circle at exactly one point, without intersecting the circle. When a line intersects a circle at exactly one point, it is called a tangent. The point of intersection is called the point of tangency. A tangent to a circle is perpendicular to the radius drawn to the point of tangency. This means that the radius and the tangent line are at right angles to each other. The length of a tangent from a point outside the circle to the circle is the same for all tangents drawn from that point. This property is useful in solving problems involving circles and tangents. The line segment joining the center of the circle to the point of tangency is called the radius. There can be only one tangent to a circle at a given point. This is because if there were two tangents at the same point, they would intersect within the circle, which is not possible. Therefore, a circle can have an infinite number of tangents, depending on the number of points outside the circle from which the tangents are drawn. The length of the tangent from a point outside the circle to the point of tangency can be found using the Pythagorean theorem. This theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Understanding the concept of circles and tangents is crucial for solving problems related to geometry and trigonometry. By applying the properties of circles and tangents, one can find the lengths of tangents, the coordinates of the point of tangency, and other related quantities.
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