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 smallest side is?

2

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Solution

The correct option is D $10$ cm
In the figure, $Δ A B C$ is the respective triangle, O is the circumcentre. $∠ A O B = 2 ∠ A C B = 2 \times 30^{o} = 60^{o}$
$\Rightarrow ∠ O A B = ∠ O B A = 60^{o} \Rightarrow Δ O A B$ is equilateral $\Rightarrow O A = A B = O B = 10$ cm.

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

The correct option is D 10 cmIn the figure, ΔABC is the respective triangle, O is the circumcentre. ∠AOB=2∠ACB=2×30o=60o⇒∠OAB=∠OBA=60o⇒ΔOAB is equilateral ⇒OA=AB=OB=10cm.

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 smallest side is?

The correct option is D $10$ cm
In the figure, $Δ A B C$ is the respective triangle, O is the circumcentre. $∠ A O B = 2 ∠ A C B = 2 \times 30^{o} = 60^{o}$
$\Rightarrow ∠ O A B = ∠ O B A = 60^{o} \Rightarrow Δ O A B$ is equilateral $\Rightarrow O A = A B = O B = 10$ cm.