Line EF is tangent to circle G at point A. If the measure of Angle CAE is 95°, what is the measure of Arc CBA?

Solution:

Given EF is the tangent to the circle G at a point A.

Also given angle CAE = 95°

To find the measure of the arc CBA.

The alternate segment theorem (also known as the tangent-chord theorem) states that in any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.

An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.

Given angle CAE = (1/2) × angle CBA

Angle CBA = 2 × angle CAE

Angle CBA = 2 × 95°

Angle CBA = 190°

Line EF is tangent to circle G at point A. If the measure of Angle CAE is 95°, what is the measure of Arc CBA?

Summary:

If the line EF is tangent to circle G at point A. If the measure of Angle CAE is 95°, then the measure of Arc CBA is 190°