# Tangents and Secants

- Author:
- James McKee

## Instructions for Part 1

Construct segment BC and measure angle EBC.

What is the relationship between the measure of arc BC and the measure of angle ECB?

## Instructions for Part 2

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).

*Hint: move the points on the circle around until arcs CD and BE are "nice" angles.*What is the relationship between the angles of at the intersection of the secants (angles CFD and EFB) and the intercepted arcs?

## Instructions for Part 3

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.

*Hint: move the points on the circle around until arcs CD and BE are "nice" angles.*What is the relationship between the angle at F and the measures of the two intercepted arcs?