Question

read the sentences below, filling in the blanks with items from this list. each item will be used once. diameter circumscribed inscribed inscribed angle theorem inscribed radius central chord 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. a circle drawn around a polygon such that all vertices of the polygon touch the circle is called a ____ circle.

Explanation:

1. An angle formed by a chord at the center of a circle is a central angle by definition.
2. A polygon that can be drawn inside a circle touching all - sides is inscribed.
3. The property that opposite angles of a cyclic quadrilateral are supplementary is a result of the Inscribed Angle Theorem.
4. An angle with its vertex on the circumference 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 that doesn't pass through the center but has endpoints on the circle is a chord.
7. The distance from the center of a circle to any point on its edge is the radius.
8. A circle drawn around a polygon such that all vertices of the polygon touch the circle is circumscribed.

Answer:

1. central
2. inscribed
3. Inscribed Angle Theorem
4. inscribed
5. diameter
6. chord
7. radius
8. circumscribed