Question

In the Fig., if $OX=\frac{1}{2}XY,PX=\frac{1}{2}XZ$ and $OX=PX$, then:

• A. $XY=YZ$
• B. $XY=XZ$
• C. $XZ=YZ$
• D. None of these

Answer 1

Answer: (B)

$XY=XZ$

Given: $OX=\frac{1}{2}XY$, $PX=\frac{1}{2}XZ$ and $OX=PX$
Now, $OX=\frac{1}{2}XY$...(I)
$\Rightarrow PX=\frac{1}{2}XZ$...(II)
From (I) and (II), we get
$\frac{1}{2}XY=\frac{1}{2}XZ$ .....(Since, $OX=PX$)
$\Rightarrow XY=XZ$