Question

In the figure, if OX = $\frac{1}{2}$XY, PX = $\frac{1}{2}$XZ and OX = PX



Then, which one of the following options is correct?

• A. XY = YZ
• B. XY = XZ
• C. XZ = YZ
• D. None of the above

Answer 1

The correct option is B XY = XZ

OX = $\frac{1}{2}$ XY ..........(1)
PX = $\frac{1}{2}$ XZ ..........(2)
OX = PX ............(3)



Things which are equal to equals are also equal to each other, from (1), (2) and (3), we get
$\frac{1}{2}$ XY = $\frac{1}{2}$XZ
Two things are equal then their doubles are also equal
$2\times \frac{1}{2}\times Y=\frac{1}{2}\times Z\times 2$
$XY=XZ$