Skip to main content
Super TutorResources
Chapter 17 of 26
Chapter Summary

Secants, Tangents And Their Properties — Chapter Summary

NIOS · Class 10 · Maths

Summary of Secants, Tangents And Their Properties for NIOS Class 10 Maths. Part of the NIOS Class 10 Maths syllabus.

35 questions26 flashcards4 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Secants, Tangents And Their Properties? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for chapter summary and more.

Try Super Tutor — Free

Free trial, no card needed.

A diagram illustrating the three possible ways a line can interact with a circle: not intersecting, intersecting at two points (secant), and touching at one point (tangent).
Super Tutor

One of 9 illustrations for Secants, Tangents And Their Properties in Super Tutor — alongside flashcards, concept maps and practice questions.

Overview

A secant intersects a circle at two distinct points, while a tangent touches a circle at exactly one point. The chapter builds the core properties of these lines, the role of the radius at the point of contact, the equal lengths of tangents drawn from an external point, the product relations for int

Key Concepts

A tangent touches a circle at

A tangent touches a circle at exactly one point, and that point is called the point of contact. A line touching a circle at one point is different fro

A secant is a line

A secant is a line that intersects a circle in two distinct points.

A tangent is the limiting position

A tangent is the limiting position of a secant when the two points of intersection coincide.

A radius through the point

A radius through the point of contact is perpendicular to the tangent at that point. Also, OP is the shortest distance from the centre O to the tangen

From a point outside a circle

From a point outside a circle, exactly two tangents can be drawn. These two tangents are equal in length and are equally inclined to the line joining

Learning Objectives

  • Define a tangent and a secant to a circle
  • Distinguish between a tangent, a secant, and an exterior line
  • Use the fact that a radius through the point of contact is perpendicular to the tangent
  • Apply the theorem that tangents from an external point are equal in length
  • Use the intersecting chords relation PA × PB = PC × PD

Frequently Asked Questions

What are the important topics in Secants, Tangents And Their Properties for NIOS Class 10 Maths?
Key topics in Secants, Tangents And Their Properties include Basic Ideas: Secant, Tangent, and Point of Contact, Tangent-Radius Property and Tangents from an External Point, Intersecting Chords and Secant-Tangent Relations, Angle Between a Tangent and a Chord. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How should I revise Secants, Tangents And Their Properties for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 35 practice questions on Secants, Tangents And Their Properties. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Secants, Tangents And Their Properties

All NIOS Class 10 Maths Chapter Summary

For serious students

Get the full Secants, Tangents And Their Properties chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for NIOS Class 10 Maths. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free