Page 1: Introduction
Circle: set of points equidistant from centre.
This chapter focuses on tangent and its properties, theorems related to tangents and chords.
High weightage — many proof and numerical questions.
Page 2: Tangent to a Circle
Tangent: line that touches circle at exactly one point.
Point of contact.
Radius perpendicular to tangent at point of contact.
Page 3: Theorem 10.1
Proof using contradiction (only one perpendicular from centre).
Page 4: Theorem 10.2
Proof using congruent triangles (two radii and common side).
Page 5: Number of Tangents from a Point
- From external point: two tangents
- From point on circle: one tangent
- From internal point: no tangent
Page 6: Length of Tangent
O = centre, r = radius.
Page 7: Tangent-Secant Theorem
Alternate segment theorem mentioned (advanced).
Page 8: Key Theorems Summary
- Theorem 10.1: radius ⊥ tangent
- Theorem 10.2: equal tangent lengths
- Tangent-secant length theorem
Page 9: Practice Questions - Easy (1-10)
- State theorem 10.1.
- Number of tangents from external point.
- Radius and tangent relation.
- Equal tangents theorem.
- Length of tangent formula.
- Tangent from point on circle.
- Draw two tangents from external point.
- Power of point meaning.
- Tangent-secant theorem statement.
- Perpendicular from centre to tangent.
Page 10: Practice Questions - Medium (11-20)
- Find length of tangent from point 13 cm from centre, r=5 cm.
- Prove theorem 10.1.
- Two tangents from point, radii 5 cm, distance 13 cm → length.
- Prove equal tangent lengths.
- Find tangent length if power 144, r=8.
- Tangent-secant numerical.
- Point outside circle, two tangents equal prove.
- Find radius if tangent length 12 cm, distance 13 cm.
- Common tangent to two circles hint.
- Verify perpendicular property.
Page 11: Practice Questions - Hard (21-30)
- Full proof of tangent-secant theorem.
- Advanced length calculation with multiple points.
- Board level proof question.
- Find point of contact coordinates.
- Combined with Pythagoras.
- Equal tangents from common point.
- Power of point advanced.
- Two circles tangent problem.
- Construction of tangent.
- Alternate segment theorem hint.
Page 12: Important Proofs Recap
Theorem 10.1 and 10.2 detailed.
Page 13: Common Mistakes
- Forgetting perpendicular property
- Wrong length formula
- Confusing tangent and secant
- Missing equal lengths
- Wrong power application
Page 14: Previous Year Questions
Prove theorems, find length, number of tangents.
Page 15: Exam Tips
- Draw neat circle with tangents
- Mark radius and perpendicular
- Show congruent triangles in proof
- Use OP² = OT² + PT²
- Memorise both theorems word by word
Page 16: Quick Revision Sheet
All theorems, formulas, properties.
Page 17: Final Motivation
Chapter 10 complete! Circles is short but important for proofs.
Master tangent length and proofs.
Class 10 Maths unstoppable 🦖
Page 18: Extra Proofs
Theorem 10.1 and 10.2 detailed.
Page 19: Length Formula Derivation
Using Pythagoras.
Page 20: Tangent-Secant Theorem
Statement and proof hint.
Page 21: Board Pattern Questions
Common proof and numerical.
Page 22: Extra Practice
More questions.
Page 23: Diagram Tips
How to draw tangents.
Page 24: Number of Tangents Cases
External, on, internal.
Page 25: Power of Point
Explanation.
Page 26: Construction of Tangent
Steps from external point.
Page 27: Thank You & Copyright
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