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Circles

Madhya Pradesh Board · Class 10 · Mathematics

Quick revision notes for Circles — Madhya Pradesh Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

133 questions56 flashcards5 concepts

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An illustration comparing the three possible positions of a line relative to a circle: non-intersecting, secant, and tangent.
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Key Topics to Revise

1

1. Positions of a Line with Respect to a Circle

  • A line with no common point with a circle is a non-intersecting line.
  • A line with two common points with a circle is a secant.
  • A line with exactly one common point with a circle is a tangent.
2

2. Theorem 10.1: Tangent is Perpendicular to Radius

  • The tangent at any point of a circle is perpendicular to the radius through the point of contact.
  • If XY is tangent to the circle at P and O is the centre, then OP ⟂ XY.
  • Take any point Q on XY other than P. Q lies outside the circle.
3

3. Number of Tangents from a Point

  • Case 1: There is no tangent to a circle passing through a point lying inside the circle.
  • Case 2: There is one and only one tangent to a circle passing through a point lying on the circle.
  • Case 3: There are exactly two tangents to a circle through a point lying outside the circle.
4

4. Theorem 10.2: Equal Tangents from an External Point

  • The lengths of tangents drawn from an external point to a circle are equal.
  • If two tangents PQ and PR are drawn from an external point P, then PQ = PR.
  • In the proof, OQ and OR are radii, so OQ = OR.

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Full Notes

Key Concepts

A line may have no commonThe common point of a tangentA tangent is a secant whenThe tangent at any pointThere is no tangent through

Frequently Asked Questions

What are the important topics in Circles for Madhya Pradesh Board Class 10 Mathematics?
Circles covers several key topics that are frequently asked in Madhya Pradesh 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 Circles — Madhya Pradesh Board Class 10 Mathematics?
Understand the core concepts first, then work through the 133 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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