Question

In the above figure, if $O$ is the centre of the circle then which of the following is correct?

• A. $x+y=z$
• B. $x=y=z$
• C. $x+y=2z$
• D. $2(x+y)=z$

Answer 1

The correct option is D $2(x+y)=z$


Let the point on circle be $A$, $B$ and $C$.
Now, minor arc $BC$ is subtending $\angle BOC$ at the centre of the circle and $\angle BAC$ at the rest part of circumference of circle.

We know the angle subtended by the arc at the centre is double the angle subtended by the same arc at any point on rest part of circumference of the circle.

So, $\angle BOC=2\angle BAC$
$z=2(x+y)$

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