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Tangents and Secants to a Circle — Syllabus

Telangana Board · Class 10 · Mathematics

What Tangents and Secants to a Circle covers in Telangana Board Class 10 Mathematics: 4 topics, for the 2026-27 session.

43 questions32 flashcards12 formulas & key relations5 concepts

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4 Topics · Telangana Board Class 10 Mathematics · 2026-27

Topics in Tangents and Secants to a Circle

1

1. Basic Ideas and Line-Circle Positions

  • A circle is a collection of all points on a plane that are at a constant distance from a fixed point.
  • There are only three possible relative positions of a line and a circle in a plane.
  • A line may be non-intersecting, a secant, or a tangent.
2

2. Tangent and Radius: Theorem 9.1

  • The tangent at any point of a circle is perpendicular to the radius through the point of contact.
  • OP is the shortest distance from the centre O to the tangent line XY, so OP is perpendicular to XY.
  • If a point Q on the tangent line lies inside the circle, then the line becomes a secant, not a tangent.
3

3. Number of Tangents and Construction from an External Point

  • There is no tangent to a circle passing through a point inside the circle.
  • There is one and only one tangent to a circle at a point on the circle.
  • There are exactly two tangents to a circle through a point outside the circle.
4

4. Angle Properties and Special Results

  • If two tangents AP and AQ are drawn to a circle with centre O from an external point A, then angle QAP = 2 angle QPO = 2 angle OQP.
  • Triangle APQ is isosceles because AP = AQ.
  • The centre lies on the bisector of the angle between the two tangents from the external point.

Key Concepts

Central concept: Tangents and Secants to a Circle

CircleLine-circle positionsSecantTangentTheorem 9.1Theorem 9.2Number of tangents from a pointConstruction of tangents

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Frequently Asked Questions

What are the important topics in Tangents and Secants to a Circle for Telangana Board Class 10 Mathematics?
Key topics in Tangents and Secants to a Circle include Basic Ideas and Line-Circle Positions, Tangent and Radius: Theorem 9.1, Number of Tangents and Construction from an External Point, Angle Properties and Special Results. Study these first, then practise questions on each for the Telangana Board Class 10 board exam.
How should I revise Tangents and Secants to a Circle for the Telangana Board Class 10 board exam?
Learn the core ideas first, then work through the 43 practice questions on Tangents and Secants to a Circle. 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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All Telangana Board Class 10 Mathematics Syllabus

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