Question

82°; edge; a segment whose endpoints are on the edge of the circle; tangent line; a line who intersects a circle twice; the vertex of an inscribed angle is on the ___ of a circle; 266°; radius; secant line; center; chord; the vertex of a central angle is on the ___ of a circle; 90°; 45°

Explanation:

To solve the circle - related vocabulary and concept - matching problems, we analyze each item:

1. "A segment whose endpoints are on the edge of the circle"

By the definition of a chord, a chord is a line segment with both endpoints on the circle. So this description matches "Chord".

2. "A line who intersects a circle twice"

A secant line is defined as a line that intersects a circle at two points. So this description matches "Secant line".

3. "The vertex of an inscribed angle is on the ____ of a circle"

An inscribed angle is an angle whose vertex lies on the circle and whose sides contain chords of the circle. So the answer for the blank is "edge" (since the vertex is on the circle, which can be described as the "edge" of the circle in this context).

4. "The vertex of a central angle is on the ____ of a circle"

A central angle is an angle whose vertex is at the center of the circle. So the answer for the blank is "center".

5. "A line that is perpendicular to the ____" (for the tangent - radius relationship)

We know that a tangent to a circle is perpendicular to the radius at the point of tangency. So the blank should be filled with "radius".

Angle - related calculations (if we assume we need to find some arc or angle measures)

For example, if we consider a circle with a central angle and an inscribed angle subtended by the same arc:

• The measure of a central angle is equal to the measure of its subtended arc.
• The measure of an inscribed angle is half the measure of its subtended arc.

If we have an inscribed angle of \(45^{\circ}\), the central angle subtended by the same arc would be \(2\times45^{\circ}=90^{\circ}\).

If we have a central angle of \(82^{\circ}\), the inscribed angle subtended by the same arc would be \(\frac{82^{\circ}}{2} = 41^{\circ}\) (if we assume the angle is acute, but if we consider the reflex angle, the major arc would correspond to an inscribed angle of \(\frac{360^{\circ}- 82^{\circ}}{2}=\frac{278^{\circ}}{2} = 139^{\circ}\), but from the given angles \(266^{\circ}\) is a reflex angle measure, and \(360^{\circ}-94^{\circ}=266^{\circ}\) (if we consider some other angle relationships).

Final Matches (key ones)

• "A segment whose endpoints are on the edge of the circle" - Chord
• "A line who intersects a circle twice" - Secant line
• "The vertex of an inscribed angle is on the ____ of a circle" - edge
• "The vertex of a central angle is on the ____ of a circle" - center
• Tangent line is perpendicular to radius at the point of tangency.

If we are asked for a specific answer, for example, the term for "A segment whose endpoints are on the edge of the circle" is "Chord".

Answer:

Chord (for the specific question about the segment with endpoints on the circle. For other parts, the answers are as analyzed above)