Question

For the given dimensions in the following figure, find the length of XW.


Here, P is the center of the circle.

• A. $\sqrt{3}$ units
• B. $\sqrt{11}$ units
• C. $\sqrt{13}$ units
• D. $13$ units

Answer 1

The correct option is B $\sqrt{11}$ units

The angle subtended by the diameter $XY$ to $Z$ on the circle is equal to ${90}^o.$

Hence, $\angle Z={90}^o,$ and $XY$ is the hypotenuse.

Given: $XZ=2\text{units},ZY=3\text{units}$
$\therefore XY=\sqrt{2^2+3^2}=\sqrt{13}\text{units}$

Similarly, for the lower half of the circle, $\angle W={90}^o.$
$\therefore X{Y}^2=X{W}^2+W{Y}^2$
$\Rightarrow X{W}^2=X{Y}^2-W{Y}^2=(\sqrt{13}{)}^2-(\sqrt{2}{)}^2$
$\Rightarrow XW=\sqrt{13-2}=\sqrt{11}\text{units}$