Combine points X and O to get segment XO and combine points Z and O to get segment ZO. Segments XO and ZO are radii of the given circle, then they are congruent. Thus, the triangle XOZ is isosceles, that gives you [tex] \angle OXZ\cong \angle OZX [/tex].
Since segments XY and YZ are tangent to the circle, then [tex] m\angle YXO=m\angle YZO=90^{\circ} [/tex].
Consider angles ∠ZXY and ∠XZY:
[tex] m\angle ZXY=m\angle OXY-m\angle OXZ,\\m\angle XZY=m\angle OZY-m\angle OZX [/tex].
Taking into account that
[tex] m\angle OXY=m\angle OZY,\\ m\angle OXZ=m\angle OZX [/tex],
you have
[tex] m\angle ZXY=m\angle XZY[/tex].
If twoo angles adjacent to the side are congruent, then this side is a base of isosceles triangle.
Answer: correct choice is B.
