NCERT Solutions Class 10 Maths Chapter 10 — Circles#
Chapter 10 explores the properties of tangents drawn to a circle. You will prove that the tangent to a circle at any point is perpendicular to the radius at that point, determine the number of tangents from an external point, and prove properties related to the lengths of tangents from an external point.
Exercises#
- Exercise 10.1 — Tangent to a circle — number of tangents from a point (4 questions)
- Exercise 10.2 — Properties and lengths of tangents from an external point (13 questions)
What you will learn#
- Tangents and secants to a circle.
- Why the tangent at any point is perpendicular to the radius through that point.
- How many tangents can be drawn from a point inside, on or outside a circle.
- Why the two tangents from an external point are equal in length.
Key formulas and results#
- Length of the tangent from an external point $P$: $PT = \sqrt{OP^2 - r^2}$, where $O$ is the centre and $r$ the radius.
Read and revise#
- Class 10 Maths Notes — Circles: every definition, formula and method in short.
- All Class 10 Maths formulas on one page.
- NCERT Class 10 Maths Chapter 10 (PDF) — the textbook chapter itself, and all Class 10 Maths chapters.
Frequently asked questions#
How many exercises are in Class 10 Maths Chapter 10?
Two: Exercise 10.1 (4 questions) and Exercise 10.2 (13 questions) — 17 questions in all, each solved step by step here.
How many tangents can a circle have?
Infinitely many — one at every point of the circle. From a point outside the circle there are exactly two, from a point on it one, and from a point inside it none.