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Chapter Summary

Secants, Tangents And Their Properties

NIOS · Class 10 · Maths

Summary of Secants, Tangents And Their Properties for NIOS Class 10 Maths. Key concepts, important points, and chapter overview.

35 questions26 flashcards5 concepts

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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).
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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 Circle-Line Relationships Overview, Secants and Tangents - Concept Overview, Circle Line Relationships Overview. These are the concepts NIOS Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Secants, Tangents And Their Properties — NIOS Class 10 Maths?
Understand the core concepts first, then work through the 35 practice questions available for this chapter. Revise formulas and 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.

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