Construct segment BC and measure angle EBC.
What is the relationship between the measure of arc BC and the measure of angle ECB?
Angle ECB is half of the measure of arc BC (or arc BC is twice as big as angle ECB).
Move around points B, C, D and E. Angles CFD and EFB are congruent to each other since they are vertical angles. Look for the relationship between those angles and the intercepted arcs (measurements displayed in degrees). [br][br][i]Hint: move the points on the circle around until arcs CD and BE are "nice" angles.[/i]
What is the relationship between the angles of at the intersection of the secants (angles CFD and EFB) and the intercepted arcs?
The angle of intersection of the secants is equal to the [b][i]average [/i][/b]of the intercepted arcs, or the [b][i]sum [/i][/b]of the intercepted arcs divided by 2.
Move points B, C, D and E around on the circle. Look for a relationship between the angle at F and the measures of the two intercepted arcs.[br][br][i]Hint: move the points on the circle around until arcs CD and BE are "nice" angles.[/i][br]
What is the relationship between the angle at F and the measures of the two intercepted arcs?
The angle at F is half of the [b][i]difference [/i][/b]between the two intercepted arcs.