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Lorico [155]
2 years ago
8

Line segments XY and ZY are tangent to circle O.

Mathematics
2 answers:
REY [17]2 years ago
3 0
It would be an Isosceles triangle
vlabodo [156]2 years ago
3 0

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 \angle OXZ\cong \angle OZX.

Since segments XY and YZ are tangent to the circle, then m\angle YXO=m\angle YZO=90^{\circ}.

Consider angles ∠ZXY and ∠XZY:

m\angle ZXY=m\angle OXY-m\angle OXZ,\\m\angle XZY=m\angle OZY-m\angle OZX.

Taking into account that

m\angle OXY=m\angle OZY,\\ m\angle OXZ=m\angle OZX,

you have

m\angle ZXY=m\angle XZY.

If twoo angles adjacent to the side are congruent, then this side is a base of isosceles triangle.

Answer: correct choice is B.

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