MathsCircle

Circle

Introduction of circle

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    Circle for Class 10th

    A circle is a shape that is formed by a set of points lying in a plane which are all the same distance from a common point called the center. The distance from any point on the circle to the center is called the radius.

    Circle Definition

    A circle is a closed curve that is characterized by all points on the curve being the same distance from a fixed point, called the center. The distance from the center to any point on the circle is called the radius.

    Circle and Line Drawn on a Plane

    The point at which the line intersects the circle is called the point of intersection.

    Tangent to a Circle

    A line that intersects a circle in only one point is called a tangent to the circle.

    Secant

    A straight line that intersects a curve at two points is called a secant.

    The following diagram shows a secant intersecting a curve at two points.

    The secant intersects the curve at points A and B.

    Tangent as an Exceptional Case of Secant

    A secant is a line that intersects two points on a curve. A tangent is a line that intersects a curve at a single point.

    A tangent is a line that intersects a curve at a single point. In the case of a circle, the tangent is perpendicular to the radius at the point of contact.

    A secant is a line that intersects two points on a curve. In the case of a circle, the secant is the line that connects the two points on the circumference of the circle that are the closest to the point of contact.

    Two Parallel Tangents at Most for a Given Secant

    There are two parallel tangents at most for a given secant.

    Number of Tangents Can be Drawn from a Given Point

    There is no definitive answer to this question. It depends on the curve and the point.

    Length of a Tangent

    A tangent is a straight line that touches a curve at a single point. The length of a tangent can be found using the following equation:

    Length of a Tangent = (Distance from Point of Tangency to Curve) / ( Tan of Angle at Point of Tangency)

    Properties of Tangent of a circle

    1. The tangent of a circle is perpendicular to the radius at the point of contact.

    2. The length of the tangent is the length of the radius.

    3. The angle between the tangent and the radius is the same as the angle between the tangent and the circle.

    Arc Length

    The length of an arc is the distance between the endpoints of the arc.

    Properties of a Circle Class 10th

    A circle is a simple closed curve consisting of all points in a plane at a fixed distance from a given point, the center. The distance from any point on the circle to the center is called the radius.

    Solved Examples Based on Circle Theorem Class 10th

    1. A contractor wants to fence in a circular area of 150 m radius. How much fencing will be needed?

    The fencing needed will be approximately 1225 m.

    Difference between the Secant of a Circle and the Chord of a Circle

    The secant of a circle is the line that intersects a circle at two points. The chord of a circle is the line that connects two points on a circle.

    Formula of the Secant of a Circle

    The secant of a circle is the length of the line segment that connects two points on the circle. The formula for the secant of a circle is:

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