Question

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

Explanation:

Step1: Use the tangent - segment theorem

The tangent - segment theorem states that if two tangent segments are drawn from an external point to a circle, then the two tangent segments are congruent.
In this case, since \(XY\) and \(ZY\) are tangent to circle \(O\) from the external point \(Y\), we have \(XY = ZY\).

Step2: Recall the definition of triangle types

• A scalene triangle has all side lengths different.
• An isosceles triangle has at least two side lengths equal.
• An equilateral triangle has all three side lengths equal.
• A right triangle has one right angle.

Since \(XY = ZY\), triangle \(XYZ\) has at least two congruent sides.

Answer:

B. an isosceles triangle