Chapter 10 · Class X Mathematics · NCERT Exercises

Circles — Exercises

Tangents · Chord Properties — All Circle Theorems Exercise-Solved

📂 3 Exercises 📝 21 Questions 🎓 Moderate-High

▶ Start Exercises 📖 Revise Notes

Exercise Index

Tangent to a circle; number of tangents from external point

Lengths of tangents from external point; tangent-chord angle; proofs

13 Q Moderate-Hard

Combined circle proofs; incircle problems; multiple tangents

3 exercise files · 21 total questions

Chapter at a Glance

CBSE BoardsNTSEOlympiad

9 Concepts

6 Formulas

Moderate-High Difficulty

6–8% Weightage

Before You Begin

Prerequisites

✓Circle basics (Class IX) — chord, arc, sector
✓Congruence of triangles
✓Pythagoras Theorem

Have Ready

🔧Compass for accurate circle drawing
🔧Ruler
🔧NCERT circle theorems card

Exercise Topic Map

Exercise 10.1 Tangent ⊥ radius at point of contact; two tangents from external point are equal

Exercise 10.2 PA=PB (tangent lengths); use congruent triangles (SSS/RHS) in proofs; angle in alternate segment

Miscellaneous AB+CD=AD+BC for quadrilateral circumscribed about circle; multi-tangent proofs

Key Formulae — Recall Before Solving

\(OT \perp PT \quad \text{(radius} \perp \text{tangent at contact point)}\)

\(PA = PB \quad \text{(tangent lengths from external point P are equal)}\)

\(OP^2 = OA^2 + AP^2 \quad \text{(right angle at A)}\)

\(AB + CD = AD + BC \quad \text{(quadrilateral circumscribed about circle)}\)

NCERT Solving Method

Step 1 — Draw a clear diagram; mark the centre O, point of contact T, and external point P. Step 2 — For tangent length problems: form right triangle OTP; apply Pythagoras. Step 3 — For proofs: use the two key theorems — (i) radius⊥tangent, (ii) tangent lengths equal; combine with congruent triangles. Step 4 — Circumscribed quadrilateral: immediately write AB+CD=AD+BC as given; use algebraically.

Continue Your Preparation

📖NotesTheory & concepts 🧠MCQsTopic-wise practice ⚖️True–FalseConcept check ➡️Next ChapterAreas Related to Circles

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NCERT Class 10 Maths Ch 10 Circles Solutions (All Exercises)

NCERT Class 10 Maths Ch 10 Circles Solutions (All Exercises) — Complete Notes & Solutions · academia-aeternum.com

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