In the Fig. 5.11, if OX = 1/2 XY, PX = 1/2 XZ and OX = PX, show that XY = XZ.

Given: OX =

⇒ 2OX = XY …(i)

PX =

⇒ 2PX = XZ

and OX =PX …(iii)

According to Euclid’s axiom, things which are double of the same things are equal to one another.

On multiplying Eq. (iii) by 2,

We get,

2 OX = 2PX

∴ XY = YZ [from Eq. (i) and (ii)]