Mathematics can be both fantastic and challenging at the same time. Specially in class 10 when students have to give board paper. So our NCERT class 10 Mathematics Chapter 10 Circles notes will provide conceptual clarity to the students. It will work like a bridge for students between class room theory lecture and solving exercise at home.
These Class 10 Chapter 10 Circles Notes is a masterstroke for students who want to pursue a career in science, like becoming an engineer, scientist etc. Most of the concept given in class 11 maths have already been introduced in class 10 maths. So these notes are also the foundation of class 11 math.
Class 10 Maths Chapter 10 Circles Notes
Below we have also given most important topics of NCERT Class 10 Mathematics chapter 10 Circles Notes. Students should revise these notes regularly to remember the chapter properly.
Important Topic of Circles
3. Tangent to the circle
A tangent to the circle is a line that intersects the circle (touches the circle) at only one point. The word ‘tangent’ comes from the Latin word ‘tangere’, which means to touch. The common point of the circle and the tangent is called point of contact.
(Diagram showing a vertical line labeled PQ touching a circle at point A)
In the figure, AB is a tangent to the circle and P is the point of contact.
4. Important facts about tangent
- The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.
- The tangent at any point of a circle is perpendicular to the radius through the point of contact. This point of contact is also called as point of tangency.
(Diagram showing a circle with a radius meeting a tangent line at right angles at the “Point of Tangency”)
- A line drawn through the end of a radius (point on circumference) and perpendicular to it is a tangent to the circle.
5. Number of tangents on a circle
- There is no tangent possible to a circle from the point (or passing through a point) lying inside the circle.
- There are exactly two tangents possible to a circle through a point outside the circle.
- At any point on the circle, there can be one and only one tangent possible.
6. Length of the tangent
The length of the segment of the tangent from the external point P and the point of contact with the circle is called the length of the tangent.
- The lengths of tangents drawn from an external point to the circle are equal.
- The figure shows two equal tangents (PA = PB) from an external point P.