Answer:
Option C is correct.
Explanation:
See the diagram attached.
Given that YZ bisects MO, hence, MZ = ZO ........ (1)
If we want to prove that point N is equidistant from points M and O, then we have to prove that Δ MNZ ≅ Δ ONZ, so that we can prove that MN = ON.
Now, to prove Δ MNZ ≅ Δ ONZ, we must have another condition that MO ⊥ YZ or, NZ ⊥ MO.
So, we have (i) MZ = OZ {from equation (1)}
(ii) ∠ NZM = ∠ NZO = 90° {Since, NZ ⊥ MO} and
(iii) NZ is the common side
Hence, by SAS criteria it is proved that Δ MNZ ≅ Δ ONZ and hence, proved that MN = ON.
Therefore, option C is correct. (Answer)