5. Alternate Segment Theorem

[b]Turn on the first checkbox: [/b]Line DE is a tangent line to the circle, perpendicular to radius OA.[br][br][b]Turn on the second checkbox: [/b]Chord AB runs from the tangent line at A to some point B on the circumference of the circle. This cuts the circle into a two segments.[br][br][b]Turn on the third checkbox: [/b]Angle BCA is the angle subtending the chord AB from point C in the alternate segment.[br][br]What do you notice about [math]\angle DAB[/math] and [math]\angle BCA[/math]?[br]Move around the points B and C to confirm this relationship?[br][br]What can you infer about the relationship between [math]\angle ABC[/math] and [math]\angle EAC[/math]?[br]Mark the checkbox to confirm the relationship between the two angles.[br][br]How would you describe the location of these angles relative to one another?[br][br]Try to prove the relationship. The auxiliary construction lines may help if you need support.

Information: 5. Alternate Segment Theorem