Question

A rectangle $ABCD$ is inscribed in a circle with centre $O$. If $AC$ is the diagonal and the $\angle BAC={30}^o$, then the radius of the circle will be equal to:

• A. $\frac{\sqrt{3}}{2}BC$
• B. $BC$
• C. $\sqrt{3}BC$
• D. $2BC$

Answer 1

The correct option is B $BC$

We know that the angle in a semicircle is ${90}^o$.

$\Rightarrow$ AC and BD are the diameters.

In $△ABC,\frac{BC}{AC}=\cos {60}^o\Rightarrow AC=2BC$
$\therefore$ Radius $=BC$