Chord AB of a circle with centre O and radius 21 mm subtends an angle of 120° at the centre. Find the perimeters of…
CBSE Class 10 Maths PYQ · Areas Related to Circles · Perimeter sector · 3 Marks · March 2026 · Standard
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403 Marks · March 2026 · Standard
Chord AB of a circle with centre O and radius $21$ mm subtends an angle of $120^\circ$ at the centre. Find the perimeters of the shaded region. (Use $\sqrt{3} = 1.73$)
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Draw $OC \perp AB$ $\therefore \angle AOC = 60^\circ$ $\sin 60^\circ = \frac{AC}{21} = \frac{\sqrt{3}}{2}$ (1 Mark) $\Rightarrow AC = \frac{21\sqrt{3}}{2}$ $\Rightarrow AB = 2 (AD) = 21\sqrt{3}$ mm (1/2 Mark) Also, length of minor arc AB = $\frac{120}{360} \times 2 \times \frac{22}{7} \times 21 = 44$ mm (1 Mark) $\therefore$ Perimeter of shaded region = $(44 + 21\sqrt{3}) = 80.33$ mm (1/2 Mark)
