Honestly please share your approach to this one in the comments below because there are at least 7 different ways you can get to the correct answer.

It’s also a good exercise in reviewing your trigonometry fundamentals.

So dig in, my friend! And when you are done trying, keep reading for the solution.

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Solution

Because the line AB is tangent to the circle, this means angle OAB must be a right-angle. Consequently, the triangle is a right triangle.

Alright guys, don’t forget your SOH-CAH-TOA and you will understand the information below.

We are given that the line BC in green bisects angle ABO, and fortunately for us, it turns out there’s an Angle Bisector Theorem, which states that

Secant is the reciprocal of cosine, so let’s multiply both sides by cosine.

Let’s take a look at the diagram again.

Well AC and OC form the radius, which is 1. So we have the following:

The answer is D. Did you come up with another method?

Let me know!