Question

The angles of a triangle are in the ratio \(2: 3: 7\) and the radius of the circumscribed circle is \(10 \mathrm{~cm}\). The length of the smallest side is
(A) \(2 \mathrm{~cm}\)
(B) \(5 \mathrm{~cm}\)
(C) \(7 \mathrm{~cm}\)
(D) \(10 \mathrm{~cm}\)

Answer 1

Ans(D)

In the figure \(\triangle \mathrm{ABC}\) is the respective triangle, \(\mathrm{O}\) is the circumcentre. \(\angle \mathrm{AOB}=2 \angle \mathrm{ACB}=2 \times 30^{\circ}=60^{\circ} \Rightarrow \angle \mathrm{OAB}=\) \(\angle \mathrm{OBA}=60^{\circ} \Rightarrow \triangle \mathrm{OAB}\) is equilateral \(\Rightarrow \mathrm{OA}=\mathrm{AB}=\mathrm{OB}=10 \mathrm{~cm}\).