Question

In the given figure, $△XYZ$ is inscribed in a circle with centre $O$. If the length of chord $YZ$ is equal to the radius of the circle $OY$, then $\angle YXZ$ is equal to

• A. ${60}^o$
• B. ${30}^o$
• C. ${80}^o$
• D. ${100}^o$

Answer 1

The correct option is B ${30}^o$

O$Y=OZ=radius=r$

Given $YZ=r$

$⟹△OYZ$ is equilateral

$⟹\angle YOZ={60}^{\circ }$

We know that angle made by a chord on any point on the circle is half the angle made by the chord at the center

$⟹\angle YXZ=\frac{\angle YOZ}{2}$

$⟹\angle YXZ=\frac{60}{2}={30}^{\circ }$