Question

line segments xy and zy are tangent to circle o. which kind of triangle must triangle xyz be? an equilateral triangle an isosceles triangle a scalene triangle a right triangle

Explanation:

Step1: Recall tangent - segment property

If two tangent segments are drawn from an external point to a circle, then the two tangent segments are equal. Here, segments $XY$ and $ZY$ are drawn from the external point $Y$ to circle $O$. So, $XY = ZY$.

Step2: Define triangle types

An equilateral triangle has all three sides equal. An isosceles triangle has at least two sides equal. A scalene triangle has no equal - sides. A right triangle has one angle equal to 90 degrees. Since $XY = ZY$, triangle $XYZ$ has at least two equal sides.

Answer:

B. an isosceles triangle