Question

the measure of an angle formed by a chord at the center of the circle is called a ______ angle.
a polygon that can be perfectly drawn inside a circle, touching all sides, is described as ______.
the ______ states that the opposite angles of a quadrilateral inscribed in a circle are supplementary.
an angle whose vertex is on the circumference of a circle and whose sides are chords is called an ______ angle.
in geometry, the distance across a circle through its center is known as the ______.
a line segment within a circle that does not pass through the center but whose endpoints lie on the circle is called a ______.
the ______ is the distance from the center of the circle to any point on its edge.

Explanation:

1. By definition, the angle formed by a chord at the center of a circle is a central angle.
2. A polygon that can be inscribed in a circle with all its vertices on the circle is called a cyclic polygon.
3. The inscribed - quadrilateral theorem states that opposite angles of a cyclic quadrilateral are supplementary.
4. An angle with its vertex on the circle and sides as chords is an inscribed angle.
5. The distance across a circle through its center is the diameter.
6. A line - segment within a circle with endpoints on the circle but not passing through the center is a chord.
7. The distance from the center of a circle to any point on its edge is the radius.

Answer:

1. central
2. cyclic polygon
3. inscribed - quadrilateral theorem
4. inscribed
5. diameter
6. chord
7. radius