Q11 of 48 Page 50

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)]


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