Question

In the given figure,

$O$ is the centre of the circle and $X$, $Y$ and $Z$ are points on circumferemce of the circle such that $\angle XZY={23}^o$. Then $\angle XOY$ is

• A. ${23}^o$
• B. ${24}^o$
• C. ${30}^o$
• D. ${46}^o$

Answer 1

The correct option is D ${46}^o$

We know: The angle subtended by an arc at the center of the circle is double the angle subtended by the same arc at any point of rest part of circumference of the circle.

So, in the given figure

Minor arc $XY$ is subtending $\angle XZY$ at the major arc $XY$ of the circle and $\angle XOY$ at the centre of the circle, so
$\angle XOY=2\angle XZY$
$\angle XOY=2\times {23}^o$
$\angle XOY={46}^o$

Hence, option $\left(d\right)$ correct.