[b][color=#0000ff][size=150]In this activity you will discover relationships in circles that involve arc and angle measures.[/size][/color][/b]

Central angles have a vertex at the center of the circle. An intercepted arc is a portion of the circumference of a circle encased by two line segments meetings at a vertex. Arcs can be measured in degrees. [br][br]Drag points A, B, and C. to determine the relationship between the degree of an arc and the central angle that creates the arc.

An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords. [br][br]In the applet below, [math]\angle[/math] BAC is an inscribed angle with an intercepted minor arc from C to B.[br]

[size=100]Move points A, B, and C to discover the relationship between the inscribed angle and the arc that the angle intercep[/size]ts. Note: that the applet above and below are two different interpretations of inscribed angles, but both are correct :)

In the activity below, create a circumscribed circle about the given triangle. This will create three inscribed angles.[br][br](To circumscribe means to draw a figure around another figure in such a way that the drawn figure touches the inside figure without intersecting.)[br][br](Hint: select the circle through 3 points tool)

Chords are segments that have both endpoints on a circle. When two chords intersect inside of a circle, four angles are formed. At the point of intersection, two sets of congruent vertical angles are formed. [br]

Engage with the applet below and move points D,C,B, and E to discover the relationship between the measure of the angles formed by intersecting chords and the measures of their intercepted arcs.

Secant lines intersect a circle at two points . The intercepted arcs are major arc DE and minor arc CB. [br]

Use the applet below and move points D,C,B, and E to discover the relationship between the measure of the angle created by two secant lines and the measure of the intercepted arcs (major and minor arcs).