Problem Solving

If the radius of a circle circumscribing a triangle is the same as one of the sides of an acute angled triangle, then what is the measure of the angle opposite the side?

A. 30
B. 45
C. 60
D. 90
E. 15

The OA is A.

I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much.

Hello AAPL.

Let's take a look at your question.

The image represents the problem. All the red lines have the same length (equal to the radius). Then, the red triangle is equilateral. Therefore, its angles have the same measure 60º.

Now, using the Central Angle Theorem, we can get that A=2*B, that is to say, $$60º=2\cdot B\ \Leftrightarrow\ \ B=30º.$$ This is why the correct answer is the option [spoiler]A=30[/spoiler].

I hope this answer can help you.

I'm available if you'd like a follow-up.

Regards.