Question

A triangle with vertices A, B, C is inscribed inside a circle such that the longest side of the triangle$\left(BC\right)$ is also the diameter of the circle. If $\angle$ABC is 30${}^{\circ }$ and the length of AC is 5cm. The diameter of the circle is:

• A. 5$\sqrt{3}$
• B. 8
• C. 10
• D. 5$\sqrt{5}$

Answer 1

The correct option is C 10

We know that the diameter subtends a ${90}^o$ angle

$\therefore in△ABC,\sin B=\frac{AC}{BC}\sin {30}^o=\frac{5}{BC}BC=10cm$.