Measuring Outside Angles Using Arcs

by

Gloria J. Thomas

 

What is the relationship between the angles formed by two secants which intersect outside the circle and the arcs they intersect?


To begin, I construct a circle using GSP sketch.  Then I add the two secants to create the triangles.

The problem here is to find the measure of exterior angle AEB.  In order to find such measure, divide the difference of arc AD and arc BC by 2 because angle DBA is one half the measure of arc AD, and angle BAC is one half the measure of arc BC.

 

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