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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 3 · Set 1 · Q27
In the given figure, chord AB subtends an angle of $\displaystyle 120$° at the centre of the circle with radius $\displaystyle 7$ cm . Find (i) perimeter of major sector OACB, and(ii)area of the shaded segment, if area of $\displaystyle \Delta \mathrm{OAB}=21 \cdot 2 \mathrm{~cm}^{2}$.
In the given figure, chord AB subtends an angle of $\displaystyle 120$° at the centre of the circle with radius $\displaystyle 7$ cm . Find (i) perimeter of major sector OACB, and
(ii)
area of the shaded segment, if area of $\displaystyle \Delta \mathrm{OAB}=21 \cdot 2 \mathrm{~cm}^{2}$.
Marking-scheme solution
(i) Perimeter of major sector = length of major arc ACB + $\displaystyle 2$ × radius
\[\begin{aligned}
& =\frac{(360-120)}{360} \times 2 \times \frac{22}{7} \times 7+2 \times 7 \\
& =\frac{130}{3} \mathrm{~cm} \text { or } 43.3 \mathrm{~cm}
\end{aligned}
\]
So, perimeter of major sector is \(\displaystyle \frac{130}{3} \mathrm{~cm}\) or $\displaystyle 43.3$ cm(ii) Area of shaded segment = Area of minor sector - Area of \(\displaystyle \triangle \mathrm{OAB}\)
\[\begin{aligned}
& =\frac{120}{360} \times \frac{22}{7} \times 7 \times 7-21.2 \\
& =30.1 \mathrm{~cm}^{2}
\end{aligned}
\] So, area of shaded segment is \(\displaystyle 30.1 \mathrm{~cm}^{2}\).
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.