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Secants, Tangents And Their Properties

NIOS · Class 10 · Maths

Quick revision notes for Secants, Tangents And Their Properties — NIOS Class 10 Maths. Key concepts, formulas, and definitions for last-minute revision.

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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Key Topics to Revise

1

1. Basic Ideas: Secant, Tangent, and Point of Contact

  • A line that does not intersect a circle is an exterior line.
  • A line that intersects a circle in two distinct points is a secant.
  • A line that touches a circle at exactly one point is a tangent.
2

2. Tangent-Radius Property and Tangents from an External Point

  • A radius through the point of contact is perpendicular to the tangent.
  • OP is the shortest distance from the centre to the tangent line, so OP is perpendicular to the tangent.
  • At the point of contact, the angle between the radius and the tangent is 90 degrees.
3

3. Intersecting Chords and Secant-Tangent Relations

  • If two chords AB and CD of a circle intersect at a point P inside or outside the circle, then PA × PB = PC × PD.
  • The same intersecting chords relation works whether the point of intersection is inside or outside the circle.
  • If PAB is a secant to a circle intersecting the circle at A and B, and PT is a tangent to the circle at T, then PA × PB = PT^2.
4

4. Angle Between a Tangent and a Chord

  • The angle formed in the alternate segment by a chord through the point of contact of a tangent equals the angle between the chord and the tangent.
  • This is the Alternate Segment Theorem.
  • The angle on one side of the chord with the tangent equals the angle in the opposite segment.

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Full Notes

Key Concepts

A tangent touches a circle atA secant is a lineA tangent is the limiting positionA radius through the pointFrom a point outside a circle

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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