Chord AB subtends an angle of 120° at the centre O of the circle with radius 21/2 cm. Find the perimeter of shaded…
CBSE Class 10 Maths PYQ · Areas Related to Circles · Segment Area · 3 Marks · March 2026 · Standard
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833 Marks · March 2026 · Standard
Chord AB subtends an angle of $120^\circ$ at the centre O of the circle with radius $\frac{21}{2}$ cm. Find the perimeter of shaded segment ACB. (Use $\sqrt{3} = 1.7$)
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Draw OD $\perp$ AB $\therefore \angle AOD = 60^\circ$ $\sin 60^\circ = \frac{\sqrt{3}}{2} = \frac{AD}{\frac{21}{2}}$ (I) (1 Mark) $\Rightarrow AD = \frac{21\sqrt{3}}{4}$ cm (II) (1/2 Mark) AB = $2 \times AD = \frac{21\sqrt{3}}{2}$ cm Also, length of minor arc AB $= \frac{120}{360} \times 2 \times \frac{22}{7} \times \frac{21}{2} = 22$ cm (III) (1 Mark) $\therefore$ Perimeter of shaded region = $(22 + \frac{21\sqrt{3}}{2}) = 39.85$ cm (IV) (1/2 Mark)
