Introduction
Ace FBISE Class 10 Mathematics Unit 10, Tangents to a Circle, under the NBF new book for the 2025 syllabus, with 90 plus marks assured through fast and accurate exam focused solutions. This page covers Exercise 10.1 and Exercise 10.2, along with the Miscellaneous Exercise, giving students a complete, quick revision tool for the entire unit.
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HSA Notes Features
- 100 percent correct as per the NBF and FBISE syllabus.
- All of Exercise 10.1, Exercise 10.2, and the Miscellaneous Exercise, fully solved.
- Short, exam ready answer format.
- Full coverage of tangent properties, tangent lengths, and circles touching internally and externally.
- Updated for the 2025 syllabus.
- Free PDF available with complete diagrams.
- Trusted by students aiming for top scores.
Target Audience
Built for FBISE and Punjab Boards students, including those at top schools such as Beaconhouse, Roots, Lahore Grammar School, The City School, Karachi Grammar School, Aitchison, Lawrence College, ICG, Army Public School, and FPS.
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Exercise 10.1, Key Solved Answers
| Q. No | Answer |
|---|---|
| Q1(i) | r equals 5 cm |
| Q1(ii) | d equals 4 root 7 cm |
| Q1(iii) | PA equals 16 cm, radius equals 8 root 3 cm |
| Q1(iv) | x equals y tan 25 degrees |
| Q1(v) | a equals 5 root 3 cm, b equals 30 cm |
| Q1(vi) | a equals b tan 30 degrees |
| Q1(vii) | a equals r tan 75 degrees |
| Q1(viii) | x equals 26 degrees, y equals 33 degrees, z equals 63 degrees |
| Q2 | (i) angle OBA equals 90 degrees, (ii) angle OCB equals 90 degrees, (iii) angle BAC equals 60 degrees, (iv) angle ABC equals 60 degrees |
| Q3 | Proved that AB equals CD |
| Q4 | Distance equals 4 ft |
| Q5 | Radii equal 2 cm, 6 cm, and 10 cm |
| Q6 | Distance equals the quantity root 319 plus 5 root 7, over 4, cm, approximately 7.77 cm |
| Q7 | Angle PGH equals 80 degrees |
| Q8 | Angle ABC equals 120 degrees |
Exercise 10.2, Key Solved Answers
| Q. No | Answer |
|---|---|
| Q1 | Angle Q equals 60 degrees, angle ROS equals 120 degrees |
| Q2 | Angle ABO equals 30 degrees, angle AOB equals 120 degrees, angle ACB equals 60 degrees |
| Q3 | Angle ABC equals 70 degrees, angle BCA equals 70 degrees, angle CAD equals 20 degrees |
| Q4 | Angle O equals 60 degrees, angle C equals 30 degrees |
| Q5 | Angle AEB equals 110 degrees, angle B equals 70 degrees, angle C equals 70 degrees, angle D equals 110 degrees |
| Q6 | (i) r equals 10 cm, (ii) angle ABE equals 60 degrees, (iii) angle ABC equals 90 degrees, (iv) angle EBD equals 30 degrees |
| Q7 | (i) scale equals 5, (ii) CQ equals 10 cm, (iii) angle BQC equals 90 degrees, angle BPO equals 90 degrees, (iv) AO equals 5 root 2 cm, (v) AR equals 5 root 2 cm |
| Q8 | (i) 60 degrees, (ii) 60 degrees, (iii) 30 degrees, (iv) 30 degrees, (v) acute, minor arc |
| Q9 | (i) 65 degrees, (ii) 65 degrees, (iii) 180 degrees |
| Q10 | (i) 95 degrees, (ii) 95 degrees, (iii) 95 degrees |
| Q11 | (i) 30 degrees, (ii) 30 degrees |
| Q12 | (i) 20 degrees, (ii) 65 degrees, (iii) 95 degrees |
| Q13 | (i) root 17 ft, (ii) root 17 minus 1 ft |
| Q14 | Diameter equals 40 cm, distance equals 40 pi cm |
Miscellaneous Exercise 10, Multiple Choice Answers
| Q. No | Answer |
|---|---|
| i | (a) 1 |
| ii | (c) perpendicular |
| iii | (b) 2 |
| iv | (b) parallel |
| v | (c) 8 cm |
| vi | (a) 1 |
| vii | (d) congruent |
| viii | (a) radii |
| ix | (b) diameter |
| x | (b) 1.1 cm |
| xi | (d) central |
| xii | (c) 90 degrees |
| xiii | (d) 50 degrees |
| xiv | (b) less than 180 degrees |
| xv | (c) greater than 180 degrees |
| xvi | (a) equal |
| xvii | (c) 120 degrees |
| xviii | (c) equal to |
| xix | (a) 45 degrees |
| xx | (d) 47 degrees |
View the full PDF for complete diagrams and proofs for every question listed above.
Why This Unit Matters for Your Overall Score
Tangents to a Circle builds directly on the chord and arc theorems from the previous unit, applying them to tangent lines, tangent lengths, and circles that touch each other internally or externally. Exercise 10.1 establishes the core tangent properties and right-angle relationships at the point of contact, which then feed into the angle chasing problems in Exercise 10.2 involving inscribed angles, cyclic quadrilaterals, and tangent-chord angles. A solid grip on this unit pays off directly in numerical problems involving unknown radii, distances, and angles, so working through both exercises in order is the fastest route to full marks.
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Frequently Asked Questions
Which exercises are covered in these Unit 10 notes?
Exercise 10.1, Exercise 10.2, and the Miscellaneous Exercise are all covered in full, with complete diagrams and proofs in the downloadable PDF.
Does this unit include both proofs and numerical problems?
Yes, Exercise 10.1 focuses on core tangent properties and tangent length relationships, while Exercise 10.2 focuses on angle based problems involving tangents, chords, and inscribed angles.
Are tangent length and circle touching problems covered?
Yes, both exercises cover tangent length calculations and problems involving circles touching internally and externally, including applied problems in feet.
Are these notes based on the current FBISE syllabus?
Yes, these notes are fully aligned with the NBF and FBISE syllabus for the 2025 session.
Conclusion
With every exercise in Unit 10 fully solved, from tangent properties through circles touching internally and externally, students have a complete resource for mastering Tangents to a Circle under the new NBF syllabus. Use these notes alongside regular practice to build both speed and accuracy ahead of your Class 10 Mathematics exam.
Best of luck for your Class 10 Mathematics exam!