[b][color=#0000ff][size=150]In this activity you will discover relationships in circles that involve arc and angle measures.[/size][/color][/b]
[b][size=100]Activity Directions: Circumscribe circles about each of the given triangles to create inscribed angles.[/size][/b]
[b][size=150][color=#0000ff]Inscribed angles are formed by two chords. The vertex of an inscribed angle is on the circle. [br][/color][/size][/b][br][b][size=100]Activity Directions: Move points A, B, and C to discover the relationship between the inscribed angle and the arc that the angle intercep[/size]ts. [/b]
[b]1. What is the relationship between an inscribed angle and the arc that the inscribed angle intercepts?[/b]
[b]Activity Directions: Inscribe circles inside each of the given triangles below to create circumscribed angles.[/b]
[b][size=150][color=#0000ff]A circumscribed angle is outside of the circle and is formed by lines that are tangent to the circle. [br][br]Lines that are tangent to a circle intersect the circle at exactly one point.[br][/color][/size][/b][br][b]Activity Directions: Move points A, B, and C below to discover the relationship between the measure of the circumscribed angle and the measures of the arcs that it intercepts.[/b]
[b]2. What is the relationship between the circumscribed angle and the arcs that it intercepts?[/b]
[b]3. What are the measures of [/b][math]\angle[/math][b]AFD and [/b][math]\angle[/math][b]AHD? Explain your reasoning.[/b]
[b][size=150][color=#0000ff]Secant lines intersect a circle at two points.[/color][/size][br][br]Activity Directions: Move points D, C, B, and E to discover the relationship between the measure of the angle created by two secant lines and the measures of the intercepted arcs. [/b]
[b]4. What is the relationship between the measure of the angle formed by two secant lines and the measures of the intercepted arcs?[/b]
[b][color=#0000ff][size=150]Chords are segments that have both endpoints on a circle.[/size][/color][/b][br][br][b]Activity Directions: 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. [/b]
[b]5. What is the relationship between the measures of angles formed by chords and the measures of their intercepted arcs?[/b]
[b]6. How do you find the angle measure of an angle inside of a circle if you know the measures of the intercepted arcs?[br][br]7. How do you find the angle measure of an angle outside of a circle if you know the measures of the intercepted arcs?[/b]