Question

read the sentences below, filling in the blanks with items from this list. each item will be used once. radius inscribed angle theorem inscribed diameter circumscribed chord central inscribed 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.
2. A polygon inside a circle touching its sides is inscribed.
3. The property about opposite - angles of an inscribed quadrilateral is from the Inscribed Angle Theorem.
4. An angle with vertex on the circle's 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 in a circle with endpoints on the circle but not through the center is a chord.
7. The distance from the circle's center to its edge is the radius.
8. A circle drawn around a polygon with all vertices touching it is a circumscribed circle.

Answer:

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