Exploring Chords

Use the 3 circles below to establish rules and properties involving chords of a circle. In the left picture, drag E to manipulate the picture. Create a conjecture about chord length and central angle measure, then click on the checkbox and drag E again. What happens to the central angles as you drag E about? Upper Right: In this illustration make a conjecture about the angle measures of a quadrilateral inscribed within a circle. Click on the hint button to emphasize sets of angles. Click the "refresh" button to restore the picture to its original state. Lower Right: Drag L to change the size of the picture. What do you note about the changing chord lengths? Write a conjecture about their lengths, the click on the checkbox and manipulate the picture again.
Alex Dostal Platteview High School Springfield, NE