These comprehensive RBSE Class 10 Maths Notes Chapter 10 Circles will give a brief overview of all the concepts.
RBSE Class 10 Maths Chapter 10 Notes Circles
1. Circle – A circle is a collection of all points in a plane which are at a constant distance from a fixed point given in that plane. A circle whose centre is O and radius is r is generally denoted by C (0, r).
2. Secant – A line which intersects the circle in two distinct points is called a secant of the circle. In the figure, AB is a secant.
3. Tangent – A tangent to a circle is a line that intersects the circle at only one point.
4. There is one and only one tangent at a point of the circle.
5. The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.
6. Theorem 1 – The tangent at any point of a circle is perpendicular to the radius through the point of contact.
(i) By theorem above, we can also conclude that at any point of a circle there can be one and only one tangent.
(ii) The line containing the radius through the point of contact is also called the ‘normal’ to the circle at that point.
7. Theorem 2 (Converse of Theorem 1)—A line that passes through an end of a radius and is perpendicular to it, is tangent to the circle.
Corollary—The perpendicular drawn at the point of contact to the tangent to the circle passes through the centre of the circle.
8. Number of Tangents from a point of a Circle
Case I—There is no tangent to a circle passing through a point lying inside the circle.
Case -II—There is one and only one tangent to a circle passing through a point lying on the circle.
Case III—There are exactly two tangents to a circle through a point lying outside the circle.
9. Theorem 3 – The length of tangents drawn from an external point to a circle are equal. It implies the following inferences—
(i) The two tangents drawn from an external point to a circle make equal angles with the line joining this point with the centre of the circle.
(ii) The tangent segments drawn from an external point to a circle extend equal angles at the centre.