You are here:

- Home
- Science
- Math for Kids
- Geometry
- Quick Word Problem

Advertisement

A circle of radius 6 has chord of length 6. If point C is selected randomly on the circle, what is the probability that ABC is obtuse?

To get a right triangle, the other point must involve a side going through the center of the circle. The length of the side going through the center is the length of the diameter, and that is twice the length of the radius. This means the length of that side is 12, and that is the hypotenuse of the triangle. If one side is 6, and the hypotenuse is 12, that means the other side is 6*square-root(3).

The other point, then, could occur anywhere closer than 6*square-root(3) from either side.

That gives the 2*6*root(3) + 6 as where the point could not appear.

Using Excel, the circumference is C = 2*pi*r = 37.69911184. Now A = 6 + 12*root(3) = 26.78460969. The region that gives an obtuse triangle is A/C = 0.710483839.

That is around 71% of the time, the triangle will be obtuse.

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |

Comment | He responded very quickly |

I can answer whatever questions you ask except how to trisect an angle. The ones I can answer include constructing parallel lines, dividing a line into n sections, bisecting an angle, splitting an angle in half, and almost anything else that is done in geometry.

I have been assisting people in Geometry since the 80's.
**Education/Credentials**

I have an MS at Oregon State and a BS at Oregon State, both with honors.
**Awards and Honors**

I was the outstanding student in high school in the area of geometry and math in general.
**Past/Present Clients**

Over 8,500 people, mostly in math, with almost 450 in geometry.