Segment Measures in Relation to Circles

Topic:
Circle
Interact with the diagram below to answer the following questions. You can adjust the circles by dragging its points. Part 1: Circle 1 shows two chords intersecting in the interior of the circle. What do you notice about the lengths of the pieces of each chord (AE and EC versus BE and ED)? Based on your findings, what can you conclude about the relationship between the two chords? Record (HINT: Play around with the pieces of the chord measures. Try adding, subtracting, multiplying them, etc. to see if you can find a relationship.) Part 2: Circle 2 shows two secants intersecting the exterior of the circle. What do you notice about the measures of the entire secant and its external peice (LI and LJ) versus (LH and LK). Based on your findings, what can you conclude about the relationship between the secant and its external segment for each secant? Part 3: Circle 3 shows a secant and a tangent intersecting in the exterior of the circle. What do you notice about the tangent (WX) versus the entire secant and its external piece (WY and WZ)? Based on your findings, what can you conclude about the relationship between the tangent and the secant with its external segment.