90+ marks in Unit 10 – fast & accurate solutions!
HSA Notes Features
- 100% NBF/FBISE correct
- Ex 10.1 + 10.2 + Misc solved
- Short exam-ready format
- Tangent properties, lengths, circles touching
- Updated 2025 syllabus
- Free PDF with diagrams
- Trusted for top scores
Target Audience
FBISE + Punjab boards. Top schools: Beaconhouse, Roots, LGS, City School, Karachi Grammar, Aitchison, Lawrence, ICG, APS, FPS.
Unit 10 Key Solved Highlights
Ex 10.1
Q1(i) r = 5 cm
Q1(ii) d = 4√7 cm
Q1(iii) PA = 16 cm, radius = 8√3 cm
Q1(iv) x = y tan 25°
Q1(v) a = 5√3 cm, b = 30 cm
Q1(vi) a = b tan 30°
Q1(vii) a = r tan 75°
Q1(viii) x=26°, y=33°, z=63°
Q2
(i) ∠OBA = 90°
(ii) ∠OCB = 90°
(iii) ∠BAC = 60°
(iv) ∠ABC = 60°
Q3 Proved AB = CD
Q4 Distance = 4 ft
Q5 Radii = 2 cm, 6 cm, 10 cm
Q6 Distance = (√319 + 5√7)/4 cm ≈ 7.77 cm
Q7 ∠PGH = 80°
Q8 ∠ABC = 120°
Ex 10.2
Q1 ∠Q = 60°, ∠ROS = 120°
Q2 ∠ABO = 30°, ∠AOB = 120°, ∠ACB = 60°
Q3 ∠ABC = 70°, ∠BCA = 70°, ∠CAD = 20°
Q4 ∠O = 60°, ∠C = 30°
Q5 ∠AEB = 110°, ∠B = 70°, ∠C = 70°, ∠D = 110°
Q6(i) r = 10 cm (ii) ∠ABE = 60° (iii) ∠ABC = 90° (iv) ∠EBD = 30°
Q7(i) Scale = 5 (ii) CQ = 10 cm (iii) ∠BQC = 90°, ∠BPO = 90° (iv) AO = 5√2 cm (v) AR = 5√2 cm
Q8(i) 60° (ii) 60° (iii) 30° (iv) 30° (v) Acute (minor arc)
Q9(i) 65° (ii) 65° (iii) 180°
Q10(i) 95° (ii) 95° (iii) 95°
Q11(i) 30° (ii) 30°
Q12(i) 20° (ii) 65° (iii) 95°
Q13(i) √17 ft (ii) √17 − 1 ft
Q14 Diameter = 40 cm, distance = 40π cm
Misc Ex 10
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°
xiii (d) 50°
xiv (b) less than 180°
xv (c) greater than 180°
xvi (a) equal
xvii (c) 120°
xviii (c) equal to
xix (a) 45°
xx (d) 47°
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