Ace FBISE Class 10 Math Unit 9 Circles – 90+ marks assured!
HSA Notes Features
- 100% NBF/FBISE aligned
- All Ex 9.1–9.4 + Misc solved
- Short, exam-focused answers
- Updated 2025 syllabus
- Chords, arcs, sectors, segments
- Quick revision tool
- Free PDF with diagrams
- Trusted for top scores
Target Audience
FBISE + Punjab boards students. Top schools: Beaconhouse, Roots, LGS, City School, Karachi Grammar, Aitchison, Lawrence, ICG, APS, FPS.
Unit 9 Key Solved Highlights
Ex 9.1
Q1 Equilateral triangle side 5 cm → unique circumcircle, radius 5√3/3 cm
Q2(i) x=4 cm, DB=4 cm
Q2(ii) y=6 cm, EF=16 cm
Q3 CD=26 cm, CE=1 cm
Q4 CD=24 cm
Q5 AB=24 cm
Q6 Smaller radius=6 cm, difference=4 cm
Q7 Distance=31 cm
Q8 r=√10 cm
Q9 Distance=5+√133 cm
Q10 Proved using Pythagoras
Q11 Proved AC=BC
Ex 9.2
Q1 ffOCF=15°, ffCFD=75°
Q2 Distance=√5 cm, equal
Q3 Distance=7 cm
Q4(i) a=12 cm, y=9 cm
Q4(ii) x=8 cm, y=10 cm, a=6 cm
Q5 7 cm
Q6 4 cm
Q7 Distance=√5 cm
Q8 Distance=31 cm
Ex 9.3
Q1(i) Yes (ii) Yes (iii) AB<AD
Q2 Proved AB ff CD
Q3 Proved arc AB=arc CD
Q4(i) No (ii) 1:2 (iii) Similar
Q5(i) Yes (ii) CD=4 cm (iii) √5 cm
Q6 120°
Q7 Proved
Q8 r=6 cm
Q9 Proved AC=BD
Q10 Proved
Q11(a) 100° (b) 100° (c) 80° (d) 40°
Q12 Proved square
Q13 ffAOB=100°, ffCOD=100°, equal
Q14(i) Proved (ii) 90° (iii) 90° (iv) Square (v) One
Ex 9.4
Q1(i) Minor=35π/9 cm, major=91π/9 cm (ii) 14π cm, yes
Q2(i) 32π/3 cm², 160π/3 cm² (ii) 64π cm², yes
Q3 25π/3 cm
Q4(i) 7π cm (ii) 10π/3 cm (iii) 11π/3 cm (iv) 49π/2 cm² (v) 50π/3 cm² (vi) 47π/6 cm²
Q5(i) 14√2 cm (ii) 7π cm (iii) 7π+14√2 cm (iv) 49 cm² (v) 49π cm² (vi) 49(π-1) cm²
Q6 4π cm
Q7 4 cm
Q8 Area=3.92π ft², perimeter=2.8π+5.6 ft
Q9 31.7 m
Q10 88/π m
Q11 Perimeter=6.96 ft, distance=0.7 ft, area=11.97 ft²
Q12 (28π)/3 ft
Q13(i) 870.25π m² (ii) 177π/20 m
Misc Ex 9
i(b) 3
ii(d) infinite
iii(c) perpendicular
iv(c) 5 cm
v(b) bisects
vi(a) centre
vii(d) chords
viii(a) 3 cm
ix(d) 13 cm
x(c) 6.6 cm
xi(b) central
xii(c) congruent
xiii(b) major
xiv(d) 90°
xv(b) 36°
xvi(d) infinite
xvii(b) same
xviii(d) >180°
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