Explore polygons that can be created by radii and chords by following these steps.

✓ 1. Move point X to point B and point Z to point A and observe the inscribed polygon.

Note that XZ is a diameter of the circle. The polygon inscribed in the circle is a triangle quadrilateral .

✓ 2. Move point Y and observe what happens to the measure of angle XYZ.

Angle XYZ is always an acute a right an obtuse angle.

✓ 3. Angle XYZ now intercepts an arc that is greater than half the circle. The polygon is a triangle quadrilateral .