Question

The figure below shows a partially completed construction of triangle XYZ.



The length of all three sides of the triangle is the same as the radius of the circle because all three points lie on or inside the arc.

The length of XY is less than the length of XZ because Y lies inside the arc and Z lies on the arc.

Two angles in the triangle are congruent because segment XY and segment XZ are of the same length.

Angle YXZ measures less than 90˚ because X is the center of the circle on which the other two vertices lie.