Question

questions: a. how did you identify and name the radius, diameter, and chord? how about the semicircle, minor arc, and major arc? inscribed angle and central angle? b. how do you describe a radius, diameter, and chord of a circle? how about the semicircle, minor arc, and major arc? inscribed angle and central angle

Explanation:

a. A radius is a line - segment from the center of a circle to a point on the circle. It is named by using the center and the point on the circle (e.g., $OA$ where $O$ is the center and $A$ is a point on the circle). A diameter is a chord that passes through the center of the circle and is named using two points on the circle that are endpoints of the diameter (e.g., $AB$). A chord is a line - segment whose endpoints lie on the circle. A semi - circle is half of a circle, named by using the two endpoints of the diameter (e.g., semi - circle $\overset{\frown}{AB}$). A minor arc is an arc that is less than a semi - circle and is named using two points on the circle (e.g., $\overset{\frown}{AB}$ for a minor arc). A major arc is an arc that is greater than a semi - circle and is named using three points on the circle (e.g., $\overset{\frown}{ACB}$). An inscribed angle is an angle whose vertex lies on the circle and whose sides are chords of the circle. A central angle is an angle whose vertex is the center of the circle and whose sides are radii of the circle.
b. A radius is a line - segment connecting the center of a circle to a point on the circle. It determines the size of the circle. A diameter is the longest chord in a circle, passing through the center and equal to twice the radius. A chord is a line - segment with endpoints on the circle. A semi - circle is half of the circular region, bounded by a diameter and an arc. A minor arc is an arc shorter than a semi - circle, and a major arc is an arc longer than a semi - circle. An inscribed angle is formed by two chords with its vertex on the circle, and a central angle is formed by two radii with its vertex at the center of the circle.

Answer:

a. Radius: line - segment from center to circle point, named with center and circle point. Diameter: chord through center, named with two circle points. Chord: line - segment with circle endpoints. Semi - circle: half of circle, named with diameter endpoints. Minor arc: arc < semi - circle, named with two circle points. Major arc: arc > semi - circle, named with three circle points. Inscribed angle: vertex on circle, sides are chords. Central angle: vertex at center, sides are radii.
b. Radius: connects center and circle point. Diameter: longest chord through center, twice radius. Chord: endpoints on circle. Semi - circle: half of circle. Minor arc: shorter than semi - circle. Major arc: longer than semi - circle. Inscribed angle: vertex on circle, formed by chords. Central angle: vertex at center, formed by radii.