State whether the following statement is true or false:
Only one line can pass through a single point.

Read the following axioms:
$(i)$ Things which are equal to the same thing are equal to one another.
$(ii)$ If equals are added to equals,the wholes are equal.
$(iii)$ Things which are double of the same thing are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.

Consider the following statement: "There exists a pair of straight lines that are everywhere equidistant from one another." Is this statement a direct consequence of Euclid's fifth postulate? Explain.

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

Give a definition for the radius of a circle. Are there other terms that need to be defined first? What are they,and how might you define them?

In the given figure,$C$ is the midpoint of $AB$ and $D$ is the midpoint of $AC$. Prove that $AD = \frac{1}{4} AB$. Mention the Euclid's axioms used in it.