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Tangents and Secants to a Circle

Telangana Board · Class 10 · Mathematics

Complete topic list for Tangents and Secants to a Circle in Telangana Board Class 10 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

44 questions32 flashcards5 concepts

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4 Topics · Telangana Board Class 10 Mathematics

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

Frequently Asked Questions

What are the important topics in Tangents and Secants to a Circle for Telangana Board Class 10 Mathematics?
Tangents and Secants to a Circle covers several key topics that are frequently asked in Telangana Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Tangents and Secants to a Circle — Telangana Board Class 10 Mathematics?
Understand the core concepts first, then work through the 44 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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