Question

If the length of the chord $YZ$ is equal to the radius of the circle $OY$, find $\angle YXZ$

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

Answer 1

The correct option is B ${30}^{\circ }$

R.E.F image

As $OY=YZ=OZ$ (given)

$\Rightarrow OYZ$ is an equilateral $\Delta \therefore \varphi ={60}^{\circ }$

As angle subtended by a chord at center is twice the angle

subtended at any other pt. on circumference $\Rightarrow \varphi =2\theta$

$\Rightarrow \theta ={30}^{\circ }$