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 triangle

Answer 1

Isosceles.

Reason: Tangents drawn from the same external point are equal in length, so XY = YZ. Therefore triangle XYZ has two equal sides and is isosceles.