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  4. The angles of a triangle are in the ratio 2: 3: 7 and the radius of the circumscribed circle is 10 cm. The length of the smallest side is

Q. The angles of a triangle are in the ratio 2 : 3 : 7 and the radius of the circumscribed circle is 10 cm. The length of the smallest side is

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Solution:

In the figure $\Delta$ABC is the respective triangle, O is the circumcentre. $∠AOB = 2∠ACB = 2 × 30^{\circ} = 60^{\circ} \Rightarrow ∠OAB = ∠OBA = 60^{\circ} \Rightarrow \Delta OAB$ is equilateral $\Rightarrow OA = AB = OB = 10\, cm.$

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