Question

Circle O is shown. Tangents C B and A B intersect at point B outside of the circle. The measure of the first arc formed is 126 degrees, and the measure of the second arc formed is 234 degrees. In the diagram of circle O, what is the measure of ? 27° 54° 108° 120°

Answer 1

Answer: b

Explanation:

Answer 2

Answer: SECOND OPTION.

Explanation:

By definition, the Angle Formed the by the intersection of two Tangents outside of a circle can be calculated with the following formula:

`Angle\ formed\ by\ two\ Tangents=(1)/(2)(Difference\ of\ intercepted\ Arcs)`

In this case, based on the information you provided in the exercise, we know that:

`Angle\ formed\ by\ two\ Tangents=\angle ABC\\\\Difference\ of\ intercepted\ Arcs=234\°-126\°\\\\Difference\ of\ intercepted\ Arcs=108\°`

Knowing those values, you can substitute them into the formula, you get:

`Angle\ formed\ by\ two\ Tangents=(1)/(2)(Difference\ of\ intercepted\ Arcs)\\\\\angle ABC=(1)/(2)(108\°)\\\\\angle ABC=54\°`