These notes for CBSE Class 10 Mathematics, Chapter 10, focus on Circles. A circle is defined as the path of points equidistant from a fixed point. The chapter introduces a secant as a line intersecting a circle at two distinct points, noting a line can meet a circle at most twice. A tangent is defined as a line touching a circle at exactly one point, called the point of contact. Key remarks highlight that points other than the contact point lie outside the circle, no tangent can be drawn from an inside point, and only one tangent exists at a point on the circumference. Two tangents can be drawn from an external point. The notes also cover two important theorems: 1. The tangent at any point is perpendicular to the radius through the point of contact. 2. The lengths of tangents drawn from an external point to a circle are equal. These notes are ideal for quick revision before exams.
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The path of all points that are equidistant from a fixed point is called a circle.
A line which intersects a circle in two distinct points is called a secant of the circle.
NOTE :- A line can meet a circle at most in two distinct points.
A line which meets a circle exactly at one point is called a tangent to the circle. In adjoining figure, the line BAC is a tangent to the circle with centre O.
NOTE :- The point where the line touches the circle is called its point of contact. In the figure
‘A’ is the point of contact.
REMARKS:
1. All points other than the point of contact of a tangent to a circle lie outside the circle.
2. No tangent can be drawn to a circle through a point inside the circle.
3. Not more than one tangent can be drawn to a circle at a point on the circumference of the circle.
4. Two tangents can be drawn to a circle from a point outside the circle.
AB and AC are two tangents drawn from the point A to the circle with centre 0.
NOTE :- The distance AB (or AC) is called the length of tangent.
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
We have given a circle with centre 0 and a tangent XY to the circle at a point P then OP i perpendicular to XY.
The lengths of tangents drawn from an external point to a circle are equal. We have a circle with centre 0, a point P lying outside the circle and two tangents PQ, PR on the circle from P then PQ = PR.
A circle is the path of all points that are equidistant from a fixed point.
A secant is a line that intersects a circle at two distinct points.
A tangent is a line that touches a circle at exactly one point, known as the point of contact.
No, a tangent cannot be drawn to a circle through a point inside the circle.
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
The lengths of tangents drawn from an external point to a circle are equal.
The point where a tangent line touches the circle is called its point of contact.
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