Question

Line segments XY and ZY are tangent to circle O.

Circle O is shown. Triangle X Y Z has points X and Z on the circle. Lines X Y and Z Y are tangents that intersect at point Y outside of the circle.

Which kind of triangle must triangle XYZ be?

an equilateral triangle
an isosceles triangle
a scalene triangle
a right triangl

Answer 1

An isosceles triangle.

Reason: Tangents drawn from the same external point to a circle have equal lengths, so XY = YZ. With two equal sides, triangle XYZ is isosceles.