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Revision Notes

Secants, Tangents And Their Properties — Revision Notes

NIOS · Class 10 · Maths

Secants, Tangents And Their Properties revision notes for NIOS Class 10 Maths: 4 topics in quick points. Part of the NIOS Class 10 Maths syllabus.

35 questions26 flashcards4 formulas & key relations5 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 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.

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