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Geometric Constructions — Revision Notes

Maharashtra Board · Class 10 · Mathematics

Geometric Constructions revision notes for Maharashtra Board Class 10 Mathematics: 4 topics in quick points. Includes Construction of a Triangle Similar.

44 questions26 flashcards4 formulas & key relations5 concepts

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Key Topics to Revise

1

Construction of a Triangle Similar to a Given Triangle

  • Similar triangles have corresponding sides in the same proportion and corresponding angles equal.
  • This construction is used when a triangle is needed with a given ratio of sides.
  • The two cases are: when vertices are distinct and when one vertex is common.
2

Tangent at a Point on a Circle Using the Centre

  • A line perpendicular to the radius at its outer end is a tangent to the circle.
  • If CP is a radius and P lies on the circle, then the line through P perpendicular to CP is the tangent at P.
  • This method uses the centre of the circle.
3

Tangent at a Point on a Circle Without Using the Centre

  • This construction does not use the centre of the circle.
  • Tangent-secant angle theorem gives ∠CAB ≅ ∠BCD.
  • The converse of the tangent-secant theorem is used to prove that the line CD is the actual tangent.
4

Tangents from a Point Outside a Circle

  • If OA and OB are radii, then OA ⟂ line PA and OB ⟂ line PB.
  • Triangles OAP and OBP are right-angled triangles and OP is their common hypotenuse.
  • A circle with diameter OP is used to locate points A and B.

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Full Notes

Key Concepts

A similar triangle has corresponding sidesA line perpendicular to the radiusHere the tangent is found byIf OA and OB are radiiAn angle inscribed in a semicircle

Frequently Asked Questions

What are the important topics in Geometric Constructions for Maharashtra Board Class 10 Mathematics?
Key topics in Geometric Constructions include Construction of a Triangle Similar to a Given Triangle, Tangent at a Point on a Circle Using the Centre, Tangent at a Point on a Circle Without Using the Centre, Tangents from a Point Outside a Circle. Study these first, then practise questions on each for the Maharashtra Board Class 10 board exam.
How should I revise Geometric Constructions for the Maharashtra Board Class 10 board exam?
Learn the core ideas first, then work through the 44 practice questions on Geometric Constructions. 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.

More resources for Geometric Constructions

All Maharashtra Board Class 10 Mathematics Revision Notes

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